diff --git a/python/src/com/jetbrains/python/validation/FStringsAnnotator.java b/python/src/com/jetbrains/python/validation/FStringsAnnotator.java
index fe30e47388ad..3a4484493736 100644
--- a/python/src/com/jetbrains/python/validation/FStringsAnnotator.java
+++ b/python/src/com/jetbrains/python/validation/FStringsAnnotator.java
@@ -49,6 +49,15 @@ public class FStringsAnnotator extends PyAnnotator {
           if (fragment.getRightBraceOffset() == -1) {
             hasUnclosedBrace = true;
           }
+          for (int i = fragment.getLeftBraceOffset() + 1; i < fragment.getContentEndOffset(); i++) {
+            final char c = nodeText.charAt(i);
+            if (c == '\\') {
+              reportCharacter(nodeOffset + i, "Expression fragments inside f-strings cannot include backslashes");
+            }
+            else if (c == '#') {
+              reportCharacter(nodeOffset + i, "Expressions fragments inside f-strings cannot include '#'");
+            }
+          }
           // Do not warn about illegal conversion character if '!' is right before closing quotes 
           if (fragContentEnd < nodeContentEnd && nodeText.charAt(fragContentEnd) == '!' && fragContentEnd + 1 < nodeContentEnd) {
             final char conversionChar = nodeText.charAt(fragContentEnd + 1);
diff --git a/python/testData/highlighting/fStringBackslashes.py b/python/testData/highlighting/fStringBackslashes.py
new file mode 100644
index 000000000000..3713a5ec9543
--- /dev/null
+++ b/python/testData/highlighting/fStringBackslashes.py
@@ -0,0 +1,5 @@
+f'{<error descr="Expression fragments inside f-strings cannot include backslashes">\</error>t}'
+f'{<error descr="Expression fragments inside f-strings cannot include backslashes">\</error>t<error descr="'}' is expected"></error>'
+f'{<error descr="Expression fragments inside f-strings cannot include backslashes">\</error>N{GREEK SMALL LETTER ALPHA}}'
+f'{Formatable():\n\t}'
+f'{42:{<error descr="Expression fragments inside f-strings cannot include backslashes">\</error>t}}'
\ No newline at end of file
diff --git a/python/testData/highlighting/fStringHashSigns.py b/python/testData/highlighting/fStringHashSigns.py
new file mode 100644
index 000000000000..6201d3648a8d
--- /dev/null
+++ b/python/testData/highlighting/fStringHashSigns.py
@@ -0,0 +1,5 @@
+f'{<error descr="Expressions fragments inside f-strings cannot include '#'">#<error descr="'}' is expected"></error></error>'
+<error descr="Missing closing quote [']">f'{<error descr="Expressions fragments inside f-strings cannot include '#'">#<error descr="'}' is expected"></error></error></error>
+f'{<error descr="Expressions fragments inside f-strings cannot include '#'">#</error>foo<error descr="Expressions fragments inside f-strings cannot include '#'">#</error>}'
+f'{42:#}'
+f'{42:{<error descr="Expressions fragments inside f-strings cannot include '#'">#</error>}}'
\ No newline at end of file
diff --git a/python/testSrc/com/jetbrains/python/PythonHighlightingTest.java b/python/testSrc/com/jetbrains/python/PythonHighlightingTest.java
index d6d5e88c11db..1c5f58aa50a5 100644
--- a/python/testSrc/com/jetbrains/python/PythonHighlightingTest.java
+++ b/python/testSrc/com/jetbrains/python/PythonHighlightingTest.java
@@ -320,6 +320,16 @@ public class PythonHighlightingTest extends PyTestCase {
     runWithLanguageLevel(LanguageLevel.PYTHON36, () -> doTest(true, false));
   }
 
+  // PY-20773
+  public void testFStringHashSigns() {
+    runWithLanguageLevel(LanguageLevel.PYTHON36, () -> doTest(true, false));
+  }
+  
+  // PY-20844
+  public void testFStringBackslashes() {
+    runWithLanguageLevel(LanguageLevel.PYTHON36, () -> doTest(true, false));
+  }
+  
   // ---
   private void doTest(final LanguageLevel languageLevel, final boolean checkWarnings, final boolean checkInfos) {
     PythonLanguageLevelPusher.setForcedLanguageLevel(myFixture.getProject(), languageLevel);