Index: clang-tools-extra/clang-tidy/modernize/LoopConvertCheck.cpp
===================================================================
--- clang-tools-extra/clang-tidy/modernize/LoopConvertCheck.cpp
+++ clang-tools-extra/clang-tidy/modernize/LoopConvertCheck.cpp
@@ -791,11 +791,6 @@
               CanonicalBeginType->getPointeeType(),
               CanonicalInitVarType->getPointeeType()))
         return false;
-    } else if (!Context->hasSameType(CanonicalInitVarType,
-                                     CanonicalBeginType)) {
-      // Check for qualified types to avoid conversions from non-const to const
-      // iterator types.
-      return false;
     }
   } else if (FixerKind == LFK_PseudoArray) {
     // This call is required to obtain the container.
Index: clang-tools-extra/docs/clang-tidy/checks/modernize-loop-convert.rst
===================================================================
--- clang-tools-extra/docs/clang-tidy/checks/modernize-loop-convert.rst
+++ clang-tools-extra/docs/clang-tidy/checks/modernize-loop-convert.rst
@@ -253,3 +253,10 @@
       flag = true;
     }
   }
+
+OpenMP
+^^^^^^
+
+As range-based for loops are only available since OpenMP 5, this check should
+not been used on code with a compatibility requirements of OpenMP prior to
+version 5.
Index: clang-tools-extra/test/clang-tidy/modernize-loop-convert-basic.cpp
===================================================================
--- clang-tools-extra/test/clang-tidy/modernize-loop-convert-basic.cpp
+++ clang-tools-extra/test/clang-tidy/modernize-loop-convert-basic.cpp
@@ -369,7 +369,7 @@
     // CHECK-FIXES: for (auto Val_int_ptr : Val_int_ptrs)
   }
 
-  // This container uses an iterator where the derefence type is a typedef of
+  // This container uses an iterator where the dereference type is a typedef of
   // a reference type. Make sure non-const auto & is still used. A failure here
   // means canonical types aren't being tested.
   {
@@ -431,19 +431,22 @@
   // CHECK-FIXES: for (auto P : *Ps)
   // CHECK-FIXES-NEXT: printf("s has value %d\n", P.X);
 
-  // V.begin() returns a user-defined type 'iterator' which, since it's
-  // different from const_iterator, disqualifies these loops from
-  // transformation.
   dependent<int> V;
   for (dependent<int>::const_iterator It = V.begin(), E = V.end();
        It != E; ++It) {
     printf("Fibonacci number is %d\n", *It);
   }
+  // CHECK-MESSAGES: :[[@LINE-4]]:3: warning: use range-based for loop instead
+  // CHECK-FIXES: for (int It : V)
+  // CHECK-FIXES-NEXT: printf("Fibonacci number is %d\n", It);
 
   for (dependent<int>::const_iterator It(V.begin()), E = V.end();
        It != E; ++It) {
     printf("Fibonacci number is %d\n", *It);
   }
+  // CHECK-MESSAGES: :[[@LINE-4]]:3: warning: use range-based for loop instead
+  // CHECK-FIXES: for (int It : V)
+  // CHECK-FIXES-NEXT: printf("Fibonacci number is %d\n", It);
 }
 
 // Tests to ensure that an implicit 'this' is picked up as the container.
Index: clang-tools-extra/test/clang-tidy/modernize-loop-convert-extra.cpp
===================================================================
--- clang-tools-extra/test/clang-tidy/modernize-loop-convert-extra.cpp
+++ clang-tools-extra/test/clang-tidy/modernize-loop-convert-extra.cpp
@@ -776,17 +776,20 @@
   // CHECK-FIXES: for (auto P : *Ps)
   // CHECK-FIXES-NEXT: printf("s has value %d\n", P.X);
 
-  // V.begin() returns a user-defined type 'iterator' which, since it's
-  // different from const_iterator, disqualifies these loops from
-  // transformation.
   dependent<int> V;
   for (dependent<int>::const_iterator It = V.begin(); It != V.end(); ++It) {
     printf("Fibonacci number is %d\n", *It);
   }
+  // CHECK-MESSAGES: :[[@LINE-3]]:3: warning: use range-based for loop instead
+  // CHECK-FIXES: for (int It : V)
+  // CHECK-FIXES-NEXT: printf("Fibonacci number is %d\n", It);
 
   for (dependent<int>::const_iterator It(V.begin()); It != V.end(); ++It) {
     printf("Fibonacci number is %d\n", *It);
   }
+  // CHECK-MESSAGES: :[[@LINE-3]]:3: warning: use range-based for loop instead
+  // CHECK-FIXES: for (int It : V)
+  // CHECK-FIXES-NEXT: printf("Fibonacci number is %d\n", It);
 }
 
 } // namespace SingleIterator
@@ -991,18 +994,26 @@
   // CHECK-FIXES: for (int & I : Dep)
   // CHECK-FIXES-NEXT: auto H2 = [&]() { int R = I + 2; };
 
-  // FIXME: It doesn't work with const iterators.
   for (dependent<int>::const_iterator I = Dep.begin(), E = Dep.end();
        I != E; ++I)
     auto H3 = [I]() { int R = *I; };
+  // CHECK-MESSAGES: :[[@LINE-3]]:3: warning: use range-based for loop instead
+  // CHECK-FIXES: for (int I : Dep)
+  // CHECK-FIXES-NEXT: auto H3 = [&I]() { int R = I; };
 
   for (dependent<int>::const_iterator I = Dep.begin(), E = Dep.end();
        I != E; ++I)
     auto H4 = [&]() { int R = *I + 1; };
+  // CHECK-MESSAGES: :[[@LINE-3]]:3: warning: use range-based for loop instead
+  // CHECK-FIXES: for (int I : Dep)
+  // CHECK-FIXES-NEXT: auto H4 = [&]() { int R = I + 1; };
 
   for (dependent<int>::const_iterator I = Dep.begin(), E = Dep.end();
        I != E; ++I)
     auto H5 = [=]() { int R = *I; };
+  // CHECK-MESSAGES: :[[@LINE-3]]:3: warning: use range-based for loop instead
+  // CHECK-FIXES: for (int R : Dep)
+  // CHECK-FIXES-NEXT: auto H5 = [=]() { };
 }
 
 void captureByValue() {