diff --git a/lib/Quox/CharExtra.idr b/lib/Quox/CharExtra.idr
index a2a05a3..48c1fab 100644
--- a/lib/Quox/CharExtra.idr
+++ b/lib/Quox/CharExtra.idr
@@ -166,3 +166,10 @@ isWhitespace ch = ch == '\t' || ch == '\r' || ch == '\n' || isSeparator ch
 export
 %foreign "scheme:string-normalize-nfc"
 normalizeNfc : String -> String
+
+
+export
+isCodepoint : Int -> Bool
+isCodepoint n =
+  n <= 0x10FFFF &&
+  not (n >= 0xD800 && n <= 0xDBFF || n >= 0xDC00 && n <= 0xDFFF)
diff --git a/lib/Quox/NatExtra.idr b/lib/Quox/NatExtra.idr
index 42f627e..64248ec 100644
--- a/lib/Quox/NatExtra.idr
+++ b/lib/Quox/NatExtra.idr
@@ -4,6 +4,7 @@ import public Data.Nat
 import Data.Nat.Division
 import Data.SnocList
 import Data.Vect
+import Data.String
 
 %default total
 
@@ -52,6 +53,42 @@ parameters {base : Nat} {auto 0 _ : base `GTE` 2} (chars : Vect base Char)
   showAtBase : Nat -> String
   showAtBase = pack . showAtBase' []
 
-export
-showHex : Nat -> String
-showHex = showAtBase $ fromList $ unpack "0123456789ABCDEF"
+namespace Nat
+  export
+  showHex : Nat -> String
+  showHex = showAtBase $ fromList $ unpack "0123456789abcdef"
+
+namespace Int
+  export
+  showHex : Int -> String
+  showHex x =
+    if x < 0 then "-" ++ Nat.showHex (cast (-x)) else Nat.showHex (cast x)
+
+
+namespace Int
+  export
+  fromHexit : Char -> Maybe Int
+  fromHexit c =
+    if      c >= '0' && c <= '9' then Just $ ord c - ord '0'
+    else if c >= 'a' && c <= 'f' then Just $ ord c - ord 'a' + 10
+    else if c >= 'A' && c <= 'F' then Just $ ord c - ord 'A' + 10
+    else Nothing
+
+  private
+  fromHex' : Int -> String -> Maybe Int
+  fromHex' acc str = case strM str of
+    StrNil       => Just acc
+    StrCons c cs => fromHex' (16 * acc + !(fromHexit c)) (assert_smaller str cs)
+
+  export %inline
+  fromHex : String -> Maybe Int
+  fromHex = fromHex' 0
+
+namespace Nat
+  export
+  fromHexit : Char -> Maybe Nat
+  fromHexit = map cast . Int.fromHexit
+
+  export %inline
+  fromHex : String -> Maybe Nat
+  fromHex = map cast . Int.fromHex
diff --git a/lib/Quox/Parser/Lexer.idr b/lib/Quox/Parser/Lexer.idr
index 7ef791f..c18c4a5 100644
--- a/lib/Quox/Parser/Lexer.idr
+++ b/lib/Quox/Parser/Lexer.idr
@@ -1,6 +1,7 @@
 module Quox.Parser.Lexer
 
 import Quox.CharExtra
+import Quox.NatExtra
 import Quox.Name
 import Data.String.Extra
 import Data.SortedMap
@@ -72,29 +73,84 @@ tmatch t f = match t (T . f)
 
 
 export
-fromStringLit : String -> String
-fromStringLit = pack . go . unpack . drop 1 . dropLast 1 where
-  go : List Char -> List Char
-  go []                  = []
-  go ['\\']              = ['\\'] -- i guess???
-  go ('\\' :: 'n' :: cs) = '\n' :: go cs
-  go ('\\' :: 't' :: cs) = '\t' :: go cs
+fromStringLit : (String -> Token) -> String -> ExtToken
+fromStringLit f str =
+  case go $ unpack $ drop 1 $ dropLast 1 str of
+    Left  err => Invalid err str
+    Right ok  => T $ f $ pack ok
+where
+  Interpolation Char where interpolate = singleton
+
+  go, hexEscape : List Char -> Either String (List Char)
+
+  go []                   = Right []
+  go ['\\']               = Left "string ends with \\"
+  go ('\\' :: 'n'  :: cs) = ('\n' ::) <$> go cs
+  go ('\\' :: 't'  :: cs) = ('\t' ::) <$> go cs
+  go ('\\' :: 'x'  :: cs) = hexEscape cs
+  go ('\\' :: 'X'  :: cs) = hexEscape cs
+  go ('\\' :: '\\' :: cs) = ('\\' ::) <$> go cs
+  go ('\\' :: '"'  :: cs) = ('"'  ::) <$> go cs
   -- [todo] others
-  go ('\\' :: c :: cs)   = c :: go cs
-  go (c :: cs)           = c :: go cs
+  go ('\\' :: c :: _)     = Left "unknown escape '\{c}'"
+  go (c :: cs)            = (c ::) <$> go cs
+
+  hexEscape cs =
+    case break (== ';') cs of
+      (hs, ';' :: rest) => do
+        let hs = pack hs
+        let Just c = Int.fromHex hs
+          | Nothing => Left #"invalid hex string "\#{hs}" in escape"#
+        if isCodepoint c
+           then (chr c ::) <$> go (assert_smaller cs rest)
+           else Left "codepoint \{hs} out of range"
+      _ => Left "unterminated hex escape"
 
 private
 string : Tokenizer ExtToken
-string = tmatch stringLit (Str . fromStringLit)
+string = match stringLit $ fromStringLit Str
+
+
+%hide binLit
+%hide octLit
+%hide hexLit
 
 private
 nat : Tokenizer ExtToken
-nat = tmatch (some (range '0' '9')) (Nat . cast)
+nat = match  hexLit fromHexLit
+  <|> tmatch decLit fromDecLit
+where
+  withUnderscores : Lexer -> Lexer
+  withUnderscores l = l <+> many (opt (is '_') <+> l)
+
+  withoutUnderscores : String -> String
+  withoutUnderscores = pack . go . unpack where
+    go : List Char -> List Char
+    go []          = []
+    go ('_' :: cs) =      go cs
+    go (c   :: cs) = c :: go cs
+
+  decLit =
+    withUnderscores (range '0' '9') <+> reject idContEnd
+
+  hexLit =
+    approx "0x" <+>
+    withUnderscores (range '0' '9' <|> range 'a' 'f' <|> range 'A' 'F') <+>
+    reject idContEnd
+
+  fromDecLit : String -> Token
+  fromDecLit = Nat . cast . withoutUnderscores
+
+  fromHexLit : String -> ExtToken
+  fromHexLit str =
+    maybe (Invalid "invalid hex sequence" str) (T . Nat) $
+    fromHex $ withoutUnderscores $ drop 2 str
+
 
 private
 tag : Tokenizer ExtToken
 tag = tmatch (is '\'' <+> name)      (Tag . drop 1)
-  <|> tmatch (is '\'' <+> stringLit) (Tag . fromStringLit . drop 1)
+  <|>  match (is '\'' <+> stringLit) (fromStringLit Tag . drop 1)
 
 
 
diff --git a/lib/Quox/Untyped/Scheme.idr b/lib/Quox/Untyped/Scheme.idr
index 61ca482..36fbdd4 100644
--- a/lib/Quox/Untyped/Scheme.idr
+++ b/lib/Quox/Untyped/Scheme.idr
@@ -7,6 +7,7 @@ import Quox.Pretty
 
 import Quox.EffExtra
 import Quox.CharExtra
+import Quox.NatExtra
 import Data.DPair
 import Data.List1
 import Data.String
@@ -278,28 +279,16 @@ prelude = """
 ;;;;;;
 """
 
-export
-toHex : Int -> String
-toHex x =
-  case toHex' x of
-    [<] => "0"
-    cs  => concatMap singleton cs
-where
-  toHex' : Int -> SnocList Char
-  toHex' x =
-    if x == 0 then [<] else
-    let d = x `div` 16
-        m = x `mod` 16 in
-    toHex' (assert_smaller x d) :<
-    assert_total strIndex "0123456789abcdef" m
-
 export
 escape : String -> String
-escape = concatMap esc1 . unpack where
+escape = foldMap esc1 . unpack where
   esc1 : Char -> String
-  esc1 c = if c < ' ' || c > '~' || c == '\\' || c == '"'
-              then "\\x" ++ toHex (ord c) ++ ";"
-              else singleton c
+  esc1 c =
+    if c == '\\' || c == '"' then
+      "\\" ++ singleton c
+    else if c < ' ' || c > '~' then
+      "\\x" ++ showHex (ord c) ++ ";"
+    else singleton c
 
 export covering
 defToScheme : Name -> Definition -> Eff Scheme (Maybe Sexp)
diff --git a/tests/Tests/Lexer.idr b/tests/Tests/Lexer.idr
index 910a434..499aab4 100644
--- a/tests/Tests/Lexer.idr
+++ b/tests/Tests/Lexer.idr
@@ -148,15 +148,31 @@ tests = "lexer" :- [
   ],
 
   "strings" :- [
-    lexes #" "" "# [Str ""],
-    lexes #" "abc" "# [Str "abc"],
-    lexes #" "\"" "# [Str "\""],
-    lexes #" "\\" "# [Str "\\"],
-    lexes #" "\\\"" "# [Str "\\\""],
-    todo "other escapes"
+    lexes   #" ""          "# [Str ""],
+    lexes   #" "abc"       "# [Str "abc"],
+    lexes   #" "\""        "# [Str "\""],
+    lexes   #" "\\"        "# [Str "\\"],
+    lexes   #" "\\\""      "# [Str "\\\""],
+    lexes   #" "\t"        "# [Str "\t"],
+    lexes   #" "\n"        "# [Str "\n"],
+    lexes   #" "🐉"        "# [Str "🐉"],
+    lexes   #" "\x1f409;"  "# [Str "🐉"],
+    lexFail #" "\q"        "#,
+    lexFail #" "\"         "#
   ],
 
-  todo "naturals",
+  "naturals" :- [
+    lexes   "0"           [Nat 0],
+    lexes   "123"         [Nat 123],
+    lexes   "69_420"      [Nat 69420],
+    lexes   "0x123"       [Nat 0x123],
+    lexes   "0xbeef"      [Nat 0xbeef],
+    lexes   "0xBEEF"      [Nat 0xBEEF],
+    lexes   "0XBEEF"      [Nat 0xBEEF],
+    lexes   "0xbaba_baba" [Nat 0xbabababa],
+    lexFail "123abc",
+    lexFail "0x123abcghi"
+  ],
 
   "universes" :- [
     lexes "Type0" [TYPE 0],