diff --git a/doc/lexical_structure.md b/doc/lexical_structure.md
index 93febbdb2891..a9d8b0b43990 100644
--- a/doc/lexical_structure.md
+++ b/doc/lexical_structure.md
@@ -128,16 +128,16 @@ Numeric literals can be specified in various bases.
 
 ```
    numeral    : numeral10 | numeral2 | numeral8 | numeral16
-   numeral10  : [0-9]+
-   numeral2   : "0" [bB] [0-1]+
-   numeral8   : "0" [oO] [0-7]+
-   numeral16  : "0" [xX] hex_char+
+   numeral10  : [0-9]+ ("_"+ [0-9]+)*
+   numeral2   : "0" [bB] ("_"* [0-1]+)+
+   numeral8   : "0" [oO] ("_"* [0-7]+)+
+   numeral16  : "0" [xX] ("_"* hex_char+)+
 ```
 
 Floating point literals are also possible with optional exponent:
 
 ```
-   float    : [0-9]+ "." [0-9]+ [[eE[+-][0-9]+]
+   float    : numeral10 "." numeral10? [eE[+-]numeral10]
 ```
 
 For example:
@@ -147,6 +147,7 @@ constant w : Int := 55
 constant x : Nat := 26085
 constant y : Nat := 0x65E5
 constant z : Float := 2.548123e-05
+constant b : Bool := 0b_11_01_10_00
 ```
 
 Note: that negative numbers are created by applying the "-" negation prefix operator to the number, for example:
diff --git a/src/Init/Meta.lean b/src/Init/Meta.lean
index 4f520ed30dae..629ba768f987 100644
--- a/src/Init/Meta.lean
+++ b/src/Init/Meta.lean
@@ -679,6 +679,7 @@ private partial def decodeBinLitAux (s : String) (i : String.Pos) (val : Nat) :
     let c := s.get i
     if c == '0' then decodeBinLitAux s (s.next i) (2*val)
     else if c == '1' then decodeBinLitAux s (s.next i) (2*val + 1)
+    else if c == '_' then decodeBinLitAux s (s.next i) val
     else none
 
 private partial def decodeOctalLitAux (s : String) (i : String.Pos) (val : Nat) : Option Nat :=
@@ -686,6 +687,7 @@ private partial def decodeOctalLitAux (s : String) (i : String.Pos) (val : Nat)
   else
     let c := s.get i
     if '0' ≤ c && c ≤ '7' then decodeOctalLitAux s (s.next i) (8*val + c.toNat - '0'.toNat)
+    else if c == '_' then decodeOctalLitAux s (s.next i) val
     else none
 
 private def decodeHexDigit (s : String) (i : String.Pos) : Option (Nat × String.Pos) :=
@@ -700,13 +702,16 @@ private partial def decodeHexLitAux (s : String) (i : String.Pos) (val : Nat) :
   if s.atEnd i then some val
   else match decodeHexDigit s i with
     | some (d, i) => decodeHexLitAux s i (16*val + d)
-    | none        => none
+    | none        =>
+      if s.get i == '_' then decodeHexLitAux s (s.next i) val
+      else none
 
 private partial def decodeDecimalLitAux (s : String) (i : String.Pos) (val : Nat) : Option Nat :=
   if s.atEnd i then some val
   else
     let c := s.get i
     if '0' ≤ c && c ≤ '9' then decodeDecimalLitAux s (s.next i) (10*val + c.toNat - '0'.toNat)
+    else if c == '_' then decodeDecimalLitAux s (s.next i) val
     else none
 
 def decodeNatLitVal? (s : String) : Option Nat :=
@@ -773,6 +778,8 @@ where
       let c := s.get i
       if '0' ≤ c && c ≤ '9' then
         decodeAfterExp (s.next i) val e sign (10*exp + c.toNat - '0'.toNat)
+      else if c == '_' then
+        decodeAfterExp (s.next i) val e sign exp
       else
         none
 
@@ -793,6 +800,8 @@ where
       let c := s.get i
       if '0' ≤ c && c ≤ '9' then
         decodeAfterDot (s.next i) (10*val + c.toNat - '0'.toNat) (e+1)
+      else if c == '_' then
+        decodeAfterDot (s.next i) val e
       else if c == 'e' || c == 'E' then
         decodeExp (s.next i) val e
       else
@@ -805,6 +814,8 @@ where
       let c := s.get i
       if '0' ≤ c && c ≤ '9' then
         decode (s.next i) (10*val + c.toNat - '0'.toNat)
+      else if c == '_' then
+        decode (s.next i) val
       else if c == '.' then
         decodeAfterDot (s.next i) val 0
       else if c == 'e' || c == 'E' then
diff --git a/src/Lean/Parser/Basic.lean b/src/Lean/Parser/Basic.lean
index 8dd33413de3f..7649171e922b 100644
--- a/src/Lean/Parser/Basic.lean
+++ b/src/Lean/Parser/Basic.lean
@@ -804,18 +804,45 @@ where
       else
         normalState num c s
 
+/--
+Parses a sequence of the form `many (many '_' >> many1 digit)`, but if `needDigit` is true the parsed result must be nonempty.
+
+Note: this does not report that it is expecting `_` if we reach EOI or an unexpected character.
+Rationale: this error happens if there is already a `_`, and while sequences of `_` are allowed, it's a bit perverse to suggest extending the sequence.
+-/
+partial def takeDigitsFn (isDigit : Char → Bool) (expecting : String) (needDigit : Bool) : ParserFn := fun c s =>
+  let input := c.input
+  let i     := s.pos
+  if h : input.atEnd i then
+    if needDigit then
+      s.mkEOIError [expecting]
+    else
+      s
+  else
+    let curr := input.get' i h
+    if curr == '_' then takeDigitsFn isDigit expecting true c (s.next' c.input i h)
+    else if isDigit curr then takeDigitsFn isDigit expecting false c (s.next' c.input i h)
+    else if needDigit then s.mkUnexpectedError "unexpected character" (expected := [expecting])
+    else s
+
 def decimalNumberFn (startPos : String.Pos) (c : ParserContext) : ParserState → ParserState := fun s =>
-  let s     := takeWhileFn (fun c => c.isDigit) c s
+  let s     := takeDigitsFn (fun c => c.isDigit) "decimal number" false c s
   let input := c.input
   let i     := s.pos
-  let curr  := input.get i
-  if curr == '.' || curr == 'e' || curr == 'E' then
+  if h : input.atEnd i then
+    mkNodeToken numLitKind startPos c s
+  else
+    let curr := input.get' i h
+    if curr == '.' || curr == 'e' || curr == 'E' then
+      parseScientific s
+    else
+      mkNodeToken numLitKind startPos c s
+where
+  parseScientific s :=
     let s := parseOptDot s
     let s := parseOptExp s
     mkNodeToken scientificLitKind startPos c s
-  else
-    mkNodeToken numLitKind startPos c s
-where
+
   parseOptDot s :=
     let input := c.input
     let i     := s.pos
@@ -824,7 +851,7 @@ where
       let i    := input.next i
       let curr := input.get i
       if curr.isDigit then
-        takeWhileFn (fun c => c.isDigit) c (s.setPos i)
+        takeDigitsFn (fun c => c.isDigit) "decimal number" false c (s.setPos i)
       else
         s.setPos i
     else
@@ -839,22 +866,22 @@ where
       let i    := if input.get i == '-' || input.get i == '+' then input.next i else i
       let curr := input.get i
       if curr.isDigit then
-        takeWhileFn (fun c => c.isDigit) c (s.setPos i)
+        takeDigitsFn (fun c => c.isDigit) "decimal number" false c (s.setPos i)
       else
         s.mkUnexpectedError "missing exponent digits in scientific literal"
     else
       s
 
 def binNumberFn (startPos : String.Pos) : ParserFn := fun c s =>
-  let s := takeWhile1Fn (fun c => c == '0' || c == '1') "binary number" c s
+  let s := takeDigitsFn (fun c => c == '0' || c == '1') "binary number" true c s
   mkNodeToken numLitKind startPos c s
 
 def octalNumberFn (startPos : String.Pos) : ParserFn := fun c s =>
-  let s := takeWhile1Fn (fun c => '0' ≤ c && c ≤ '7') "octal number" c s
+  let s := takeDigitsFn (fun c => '0' ≤ c && c ≤ '7') "octal number" true c s
   mkNodeToken numLitKind startPos c s
 
 def hexNumberFn (startPos : String.Pos) : ParserFn := fun c s =>
-  let s := takeWhile1Fn (fun c => ('0' ≤ c && c ≤ '9') || ('a' ≤ c && c ≤ 'f') || ('A' ≤ c && c ≤ 'F')) "hexadecimal number" c s
+  let s := takeDigitsFn (fun c => ('0' ≤ c && c ≤ '9') || ('a' ≤ c && c ≤ 'f') || ('A' ≤ c && c ≤ 'F')) "hexadecimal number" true c s
   mkNodeToken numLitKind startPos c s
 
 def numberFnAux : ParserFn := fun c s =>
diff --git a/tests/lean/run/6199.lean b/tests/lean/run/6199.lean
new file mode 100644
index 000000000000..c0702cc11857
--- /dev/null
+++ b/tests/lean/run/6199.lean
@@ -0,0 +1,107 @@
+import Lean
+/-!
+# `_` separators for numeric literals
+RFC: https://github.com/leanprover/lean4/issues/6199
+-/
+set_option pp.mvars false
+
+open Lean Elab
+
+elab "#term " s:str : command => Command.liftTermElabM <| withRef s do
+  let t ← Lean.ofExcept <| Parser.runParserCategory (← getEnv) `term s.getString
+  let e ← Term.elabTermAndSynthesize t none
+  logInfo m!"{e} : {← Meta.inferType e}"
+
+/-!
+Decimal tests
+-/
+/-- info: 0 : Nat -/
+#guard_msgs in #term "0"
+/-- info: 1 : Nat -/
+#guard_msgs in #term "1"
+/-- info: 1000000 : Nat -/
+#guard_msgs in #term "1000000"
+/-- info: 1000000 : Nat -/
+#guard_msgs in #term "1_000_000"
+/-- info: 1000000 : Nat -/
+#guard_msgs in #term "1__000___000"
+/-- error: <input>:1:5: unexpected end of input; expected decimal number -/
+#guard_msgs in #term "1_00_"
+/-- error: <input>:1:6: unexpected character; expected decimal number -/
+#guard_msgs in #term "(1_00_)"
+-- Starting with `_` is an identifier:
+/--
+error: unknown identifier '_10'
+---
+info: sorry : ?_
+-/
+#guard_msgs in #term "_10"
+
+/-!
+Scientific tests
+-/
+/-- info: 100000. : Float -/
+#guard_msgs in #term "100_000."
+/-- info: 100000.0 : Float -/
+#guard_msgs in #term "100_000.0"
+/-- info: 0. : Float -/
+#guard_msgs in #term "0."
+-- The decimal parser requires a digit at the start, so the `_` is left over:
+/-- error: <input>:1:4: expected end of input -/
+#guard_msgs in #term "100._"
+/-- info: 100.111111 : Float -/
+#guard_msgs in #term "100.111_111"
+/-- error: <input>:1:8: unexpected end of input; expected decimal number -/
+#guard_msgs in #term "100.111_"
+/-- error: <input>:1:9: unexpected character; expected decimal number -/
+#guard_msgs in #term "(100.111_)"
+/-- info: 100111111e1094 : Float -/
+#guard_msgs in #term "100.111_111e1_100"
+/-- error: <input>:1:5: unexpected end of input; expected decimal number -/
+#guard_msgs in #term "1e10_"
+/-- error: <input>:1:6: unexpected character; expected decimal number -/
+#guard_msgs in #term "(1e10_)"
+/-- error: <input>:1:1: missing exponent digits in scientific literal -/
+#guard_msgs in #term "1e_10"
+
+/-!
+Base-2 tests
+-/
+/-- info: 15 : Nat -/
+#guard_msgs in #term "0b1111"
+/-- info: 15 : Nat -/
+#guard_msgs in #term "0b11_11"
+/-- info: 15 : Nat -/
+#guard_msgs in #term "0b__11__11"
+/-- error: <input>:1:7: unexpected end of input; expected binary number -/
+#guard_msgs in #term "0b1111_"
+/-- error: <input>:1:8: unexpected character; expected binary number -/
+#guard_msgs in #term "(0b1111_)"
+
+/-!
+Base-8 tests
+-/
+/-- info: 512 : Nat -/
+#guard_msgs in #term "0o1000"
+/-- info: 512 : Nat -/
+#guard_msgs in #term "0o1_000"
+/-- info: 512 : Nat -/
+#guard_msgs in #term "0o_1_000"
+/-- error: <input>:1:7: unexpected end of input; expected octal number -/
+#guard_msgs in #term "0o1000_"
+/-- error: <input>:1:8: unexpected character; expected octal number -/
+#guard_msgs in #term "(0o1000_)"
+
+/-!
+Base-16 tests
+-/
+/-- info: 4096 : Nat -/
+#guard_msgs in #term "0x1000"
+/-- info: 4096 : Nat -/
+#guard_msgs in #term "0x1_000"
+/-- info: 4096 : Nat -/
+#guard_msgs in #term "0x_1_000"
+/-- error: <input>:1:7: unexpected end of input; expected hexadecimal number -/
+#guard_msgs in #term "0x1000_"
+/-- error: <input>:1:8: unexpected character; expected hexadecimal number -/
+#guard_msgs in #term "(0x1000_)"