diff --git a/lib/rules/selector-max-attribute/index.js b/lib/rules/selector-max-attribute/index.js
index ff4edf904a..d69db7eb47 100644
--- a/lib/rules/selector-max-attribute/index.js
+++ b/lib/rules/selector-max-attribute/index.js
@@ -2,6 +2,7 @@
 
 const _ = require("lodash");
 const hasUnresolvedNestedSelector = require("../../utils/hasUnresolvedNestedSelector");
+const isLogicalCombination = require("../../utils/isLogicalCombination");
 const isStandardSyntaxRule = require("../../utils/isStandardSyntaxRule");
 const isStandardSyntaxSelector = require("../../utils/isStandardSyntaxSelector");
 const optionsMatches = require("../../utils/optionsMatches");
@@ -48,8 +49,8 @@ function rule(max, options) {
 
     function checkSelector(selectorNode, ruleNode) {
       const count = selectorNode.reduce((total, childNode) => {
-        // Only traverse inside actual selectors and :not()
-        if (childNode.type === "selector" || childNode.value === ":not") {
+        // Only traverse inside actual selectors and logical combinations
+        if (childNode.type === "selector" || isLogicalCombination(childNode)) {
           checkSelector(childNode, ruleNode);
         }
 
diff --git a/lib/rules/selector-max-class/index.js b/lib/rules/selector-max-class/index.js
index adc8492a91..4a58d203e5 100644
--- a/lib/rules/selector-max-class/index.js
+++ b/lib/rules/selector-max-class/index.js
@@ -1,5 +1,6 @@
 "use strict";
 
+const isLogicalCombination = require("../../utils/isLogicalCombination");
 const isStandardSyntaxRule = require("../../utils/isStandardSyntaxRule");
 const isStandardSyntaxSelector = require("../../utils/isStandardSyntaxSelector");
 const parseSelector = require("../../utils/parseSelector");
@@ -34,8 +35,8 @@ function rule(max) {
 
     function checkSelector(selectorNode, ruleNode) {
       const count = selectorNode.reduce((total, childNode) => {
-        // Only traverse inside actual selectors and :not()
-        if (childNode.type === "selector" || childNode.value === ":not") {
+        // Only traverse inside actual selectors and logical combinations
+        if (childNode.type === "selector" || isLogicalCombination(childNode)) {
           checkSelector(childNode, ruleNode);
         }
 
diff --git a/lib/rules/selector-max-compound-selectors/index.js b/lib/rules/selector-max-compound-selectors/index.js
index 383ee0ff40..9f845755b5 100644
--- a/lib/rules/selector-max-compound-selectors/index.js
+++ b/lib/rules/selector-max-compound-selectors/index.js
@@ -1,5 +1,6 @@
 "use strict";
 
+const isLogicalCombination = require("../../utils/isLogicalCombination");
 const isStandardSyntaxRule = require("../../utils/isStandardSyntaxRule");
 const isStandardSyntaxSelector = require("../../utils/isStandardSyntaxSelector");
 const parseSelector = require("../../utils/parseSelector");
@@ -37,8 +38,8 @@ const rule = function(max) {
       let compoundCount = 1;
 
       selectorNode.each(childNode => {
-        // Only traverse inside actual selectors and :not()
-        if (childNode.type === "selector" || childNode.value === ":not") {
+        // Only traverse inside actual selectors and logical combinations
+        if (childNode.type === "selector" || isLogicalCombination(childNode)) {
           checkSelector(childNode, rule);
         }
 
diff --git a/lib/rules/selector-max-id/index.js b/lib/rules/selector-max-id/index.js
index 161b1a9787..a98268018c 100644
--- a/lib/rules/selector-max-id/index.js
+++ b/lib/rules/selector-max-id/index.js
@@ -1,5 +1,6 @@
 "use strict";
 
+const isLogicalCombination = require("../../utils/isLogicalCombination");
 const isStandardSyntaxRule = require("../../utils/isStandardSyntaxRule");
 const isStandardSyntaxSelector = require("../../utils/isStandardSyntaxSelector");
 const parseSelector = require("../../utils/parseSelector");
@@ -34,8 +35,8 @@ function rule(max) {
 
     function checkSelector(selectorNode, ruleNode) {
       const count = selectorNode.reduce((total, childNode) => {
-        // Only traverse inside actual selectors and :not()
-        if (childNode.type === "selector" || childNode.value === ":not") {
+        // Only traverse inside actual selectors and logical combinations
+        if (childNode.type === "selector" || isLogicalCombination(childNode)) {
           checkSelector(childNode, ruleNode);
         }
 
diff --git a/lib/rules/selector-max-pseudo-class/index.js b/lib/rules/selector-max-pseudo-class/index.js
index 98c6ea5f81..05b9fcef45 100644
--- a/lib/rules/selector-max-pseudo-class/index.js
+++ b/lib/rules/selector-max-pseudo-class/index.js
@@ -1,5 +1,6 @@
 "use strict";
 
+const isLogicalCombination = require("../../utils/isLogicalCombination");
 const isStandardSyntaxRule = require("../../utils/isStandardSyntaxRule");
 const isStandardSyntaxSelector = require("../../utils/isStandardSyntaxSelector");
 const keywordSets = require("../../reference/keywordSets");
@@ -35,8 +36,8 @@ function rule(max) {
 
     function checkSelector(selectorNode, ruleNode) {
       const count = selectorNode.reduce((total, childNode) => {
-        // Only traverse inside actual selectors and :not()
-        if (childNode.type === "selector" || childNode.value === ":not") {
+        // Only traverse inside actual selectors and logical combinations
+        if (childNode.type === "selector" || isLogicalCombination(childNode)) {
           checkSelector(childNode, ruleNode);
         }
 
diff --git a/lib/rules/selector-max-type/index.js b/lib/rules/selector-max-type/index.js
index eb6e74905a..5061dd587c 100644
--- a/lib/rules/selector-max-type/index.js
+++ b/lib/rules/selector-max-type/index.js
@@ -3,6 +3,7 @@
 const _ = require("lodash");
 const hasUnresolvedNestedSelector = require("../../utils/hasUnresolvedNestedSelector");
 const isKeyframeSelector = require("../../utils/isKeyframeSelector");
+const isLogicalCombination = require("../../utils/isLogicalCombination");
 const isOnlyWhitespace = require("../../utils/isOnlyWhitespace");
 const isStandardSyntaxRule = require("../../utils/isStandardSyntaxRule");
 const isStandardSyntaxSelector = require("../../utils/isStandardSyntaxSelector");
@@ -54,8 +55,8 @@ function rule(max, options) {
 
     function checkSelector(selectorNode, ruleNode) {
       const count = selectorNode.reduce((total, childNode) => {
-        // Only traverse inside actual selectors and :not()
-        if (childNode.type === "selector" || childNode.value === ":not") {
+        // Only traverse inside actual selectors and logical combinations
+        if (childNode.type === "selector" || isLogicalCombination(childNode)) {
           checkSelector(childNode, ruleNode);
         }
 
diff --git a/lib/rules/selector-max-universal/index.js b/lib/rules/selector-max-universal/index.js
index eb7d78b731..a332e2e85d 100644
--- a/lib/rules/selector-max-universal/index.js
+++ b/lib/rules/selector-max-universal/index.js
@@ -1,6 +1,7 @@
 "use strict";
 
 const hasUnresolvedNestedSelector = require("../../utils/hasUnresolvedNestedSelector");
+const isLogicalCombination = require("../../utils/isLogicalCombination");
 const isStandardSyntaxRule = require("../../utils/isStandardSyntaxRule");
 const isStandardSyntaxSelector = require("../../utils/isStandardSyntaxSelector");
 const parseSelector = require("../../utils/parseSelector");
@@ -36,8 +37,8 @@ function rule(max) {
 
     function checkSelector(selectorNode, ruleNode) {
       const count = selectorNode.reduce((total, childNode) => {
-        // Only traverse inside actual selectors and :not()
-        if (childNode.type === "selector" || childNode.value === ":not") {
+        // Only traverse inside actual selectors and logical combinations
+        if (childNode.type === "selector" || isLogicalCombination(childNode)) {
           checkSelector(childNode, ruleNode);
         }
 
diff --git a/lib/rules/selector-pseudo-class-blacklist/__tests__/index.js b/lib/rules/selector-pseudo-class-blacklist/__tests__/index.js
index bed8141e6b..1525970548 100644
--- a/lib/rules/selector-pseudo-class-blacklist/__tests__/index.js
+++ b/lib/rules/selector-pseudo-class-blacklist/__tests__/index.js
@@ -5,7 +5,14 @@ const { messages, ruleName } = rule;
 
 testRule(rule, {
   ruleName,
-  config: ["focus", "global", "input-placeholder", "not", "nth-last-child"],
+  config: [
+    "focus",
+    "global",
+    "input-placeholder",
+    "not",
+    "nth-last-child",
+    "has"
+  ],
   skipBasicChecks: true,
 
   accept: [
@@ -87,6 +94,12 @@ testRule(rule, {
       message: messages.rejected("not"),
       line: 1,
       column: 2
+    },
+    {
+      code: "a:has(> img) {}",
+      message: messages.rejected("has"),
+      line: 1,
+      column: 2
     }
   ]
 });
@@ -145,6 +158,51 @@ testRule(rule, {
   ]
 });
 
+testRule(rule, {
+  ruleName,
+  config: [[/(not|matches|has)/]],
+  skipBasicChecks: true,
+
+  accept: [
+    {
+      code: "a:focus {}"
+    }
+  ],
+
+  reject: [
+    {
+      code: "a:not() {}",
+      message: messages.rejected("not"),
+      line: 1,
+      column: 2
+    },
+    {
+      code: "body:not(div):not(span) {}",
+      message: messages.rejected("not"),
+      line: 1,
+      column: 5
+    },
+    {
+      code: "body:nt(div):not(span) {}",
+      message: messages.rejected("not"),
+      line: 1,
+      column: 13
+    },
+    {
+      code: "a:has() {}",
+      message: messages.rejected("has"),
+      line: 1,
+      column: 2
+    },
+    {
+      code: "a:matches() {}",
+      message: messages.rejected("matches"),
+      line: 1,
+      column: 2
+    }
+  ]
+});
+
 testRule(rule, {
   ruleName,
   config: ["variable"],
diff --git a/lib/rules/selector-pseudo-class-case/__tests__/index.js b/lib/rules/selector-pseudo-class-case/__tests__/index.js
index e457879a31..94b55845b0 100644
--- a/lib/rules/selector-pseudo-class-case/__tests__/index.js
+++ b/lib/rules/selector-pseudo-class-case/__tests__/index.js
@@ -204,6 +204,34 @@ testRule(rule, {
       line: 1,
       column: 3
     },
+    {
+      code: ":matcheS(a, .foo) { }",
+      fixed: ":matches(a, .foo) { }",
+      message: messages.expected(":matcheS", ":matches"),
+      line: 1,
+      column: 1
+    },
+    {
+      code: ":Matches(a, .foo) { }",
+      fixed: ":matches(a, .foo) { }",
+      message: messages.expected(":Matches", ":matches"),
+      line: 1,
+      column: 1
+    },
+    {
+      code: "a:hAs(> img) { }",
+      fixed: "a:has(> img) { }",
+      message: messages.expected(":hAs", ":has"),
+      line: 1,
+      column: 2
+    },
+    {
+      code: "a:HAS(> img) {\n}",
+      fixed: "a:has(> img) {\n}",
+      message: messages.expected(":HAS", ":has"),
+      line: 1,
+      column: 2
+    },
     {
       code: ":Root { background: #ff0000; }",
       fixed: ":root { background: #ff0000; }",
diff --git a/lib/rules/selector-pseudo-class-no-unknown/__tests__/index.js b/lib/rules/selector-pseudo-class-no-unknown/__tests__/index.js
index f50a613044..69901bd5fb 100644
--- a/lib/rules/selector-pseudo-class-no-unknown/__tests__/index.js
+++ b/lib/rules/selector-pseudo-class-no-unknown/__tests__/index.js
@@ -36,6 +36,9 @@ testRule(rule, {
     {
       code: ":matches(section, article, aside, nav) h1 { }"
     },
+    {
+      code: "a:has(> img) { }"
+    },
     {
       code: "section:has(h1, h2, h3, h4, h5, h6) { }"
     },
@@ -75,6 +78,9 @@ testRule(rule, {
     {
       code: "@page foo:left { }"
     },
+    {
+      code: "body:not(div):not(span) {}"
+    },
     {
       code: ":root { --foo: 1px; }",
       description: "custom property in root"
@@ -137,6 +143,12 @@ testRule(rule, {
       line: 1,
       column: 2
     },
+    {
+      code: "body:not(div):noot(span) {}",
+      message: messages.rejected(":noot"),
+      line: 1,
+      column: 14
+    },
     {
       code: "a:unknown::before { }",
       message: messages.rejected(":unknown"),
diff --git a/lib/rules/selector-pseudo-class-parentheses-space-inside/__tests__/index.js b/lib/rules/selector-pseudo-class-parentheses-space-inside/__tests__/index.js
index 3dc503188d..db683d3477 100644
--- a/lib/rules/selector-pseudo-class-parentheses-space-inside/__tests__/index.js
+++ b/lib/rules/selector-pseudo-class-parentheses-space-inside/__tests__/index.js
@@ -105,6 +105,13 @@ testRule(rule, {
       line: 1,
       column: 19
     },
+    {
+      code: ":matches( a, ul, :has(h1, h2 ) ) { }",
+      fixed: ":matches( a, ul, :has( h1, h2 ) ) { }",
+      message: messages.expectedOpening,
+      line: 1,
+      column: 23
+    },
     {
       code: "section:not( :has( h1, h2) ) { }",
       fixed: "section:not( :has( h1, h2 ) ) { }",
@@ -197,6 +204,9 @@ testRule(rule, {
     },
     {
       code: "a:hover:not(.active) { }"
+    },
+    {
+      code: ":matches(a, ul, :has(h1, h2)) { }"
     }
   ],
 
diff --git a/lib/rules/selector-pseudo-class-whitelist/__tests__/index.js b/lib/rules/selector-pseudo-class-whitelist/__tests__/index.js
index ff79db866f..7ec080f6bb 100644
--- a/lib/rules/selector-pseudo-class-whitelist/__tests__/index.js
+++ b/lib/rules/selector-pseudo-class-whitelist/__tests__/index.js
@@ -5,7 +5,7 @@ const { messages, ruleName } = rule;
 
 testRule(rule, {
   ruleName,
-  config: ["hover", "nth-child", "root", "placeholder"],
+  config: ["hover", "nth-child", "root", "placeholder", "has"],
   skipBasicChecks: true,
 
   accept: [
@@ -21,6 +21,9 @@ testRule(rule, {
     {
       code: ":root {}"
     },
+    {
+      code: "a:has(#id) {}"
+    },
     {
       code: "a:hover, a:nth-child(5) {}"
     },
diff --git a/lib/utils/__tests__/isLogicalCombination.test.js b/lib/utils/__tests__/isLogicalCombination.test.js
new file mode 100644
index 0000000000..fe5d73aee5
--- /dev/null
+++ b/lib/utils/__tests__/isLogicalCombination.test.js
@@ -0,0 +1,39 @@
+"use strict";
+
+const isLogicalCombination = require("../isLogicalCombination");
+const parseSelector = require("postcss-selector-parser");
+const postcss = require("postcss");
+
+function selector(css, cb) {
+  postcss.parse(css).walkRules(rule => {
+    parseSelector(selectorAST => {
+      selectorAST.walkPseudos(cb);
+    }).processSync(rule.selector);
+  });
+}
+
+describe("isLogicalCombination", () => {
+  it("hover pseudo class is NOT logical combination", () => {
+    selector("a:hover {}", selector => {
+      expect(isLogicalCombination(selector)).toBe(false);
+    });
+  });
+
+  it("not pseudo class is logical combination", () => {
+    selector("a:not(.foo) {}", selector => {
+      expect(isLogicalCombination(selector)).toBe(true);
+    });
+  });
+
+  it("has pseudo class is logical combination", () => {
+    selector("a:has(.foo) {}", selector => {
+      expect(isLogicalCombination(selector)).toBe(true);
+    });
+  });
+
+  it("matches pseudo class is logical combination", () => {
+    selector("a:matches(.foo) {}", selector => {
+      expect(isLogicalCombination(selector)).toBe(true);
+    });
+  });
+});
diff --git a/lib/utils/isLogicalCombination.js b/lib/utils/isLogicalCombination.js
new file mode 100644
index 0000000000..9f5e5123b2
--- /dev/null
+++ b/lib/utils/isLogicalCombination.js
@@ -0,0 +1,25 @@
+/* @flow */
+"use strict";
+
+/**
+ * Check whether a node is logical combination (`:not`, `:has`, `:matches`)
+ *
+ * @param {Node} postcss-selector-parser node (of type pseudo)
+ * @return {boolean} If `true`, the combination is logical
+ */
+module.exports = function isLogicalCombination(
+  node /*: Object*/
+) /*: boolean*/ {
+  if (node.type === "pseudo") {
+    switch (node.value) {
+      case ":not":
+      case ":has":
+      case ":matches":
+        return true;
+      default:
+        return false;
+    }
+  }
+
+  return false;
+};