diff --git a/monoidal-containers.cabal b/monoidal-containers.cabal
--- a/monoidal-containers.cabal
+++ b/monoidal-containers.cabal
@@ -1,5 +1,5 @@
 name:                monoidal-containers
-version:             0.1.2.5
+version:             0.2.0.0
 synopsis:            Containers with monoidal accumulation
 description:         Containers with monoidal accumulation
 homepage:            http://github.com/bgamari/monoidal-containers
@@ -11,6 +11,7 @@
 category:            Data
 build-type:          Simple
 cabal-version:       >=1.10
+tested-with:         GHC ==7.4.2, GHC ==7.6.3, GHC ==7.8.4, GHC ==8.0.1
 
 source-repository head
   type:                git
@@ -24,9 +25,9 @@
                        GeneralizedNewtypeDeriving,
                        DeriveTraversable,
                        DeriveDataTypeable
-  build-depends:       base >=4.7 && <4.10,
+  build-depends:       base >=4.5 && <4.10,
                        deepseq >=1.3 && <1.5,
-                       containers >=0.5 && <0.6,
+                       containers >=0.4 && <0.6,
                        unordered-containers >= 0.2 && < 0.3,
                        hashable >= 1.2 && < 1.3,
                        lens >=4.4 && <5,
diff --git a/src/Data/HashMap/Monoidal.hs b/src/Data/HashMap/Monoidal.hs
--- a/src/Data/HashMap/Monoidal.hs
+++ b/src/Data/HashMap/Monoidal.hs
@@ -12,12 +12,14 @@
 --
 -- While some functions mirroring those of 'Data.HashMap' are provided
 -- here for convenience, more specialized needs will likely want to use
--- either the @Newtype@ or @Wrapped@ instances to manipulate the
+-- either the 'Newtype' or 'Wrapped' instances to manipulate the
 -- underlying 'Map'.
 
 module Data.HashMap.Monoidal
     ( MonoidalHashMap
       -- * Often-needed functions
+    , toList
+    , fromList
     , singleton
     , size
     , member
@@ -30,9 +32,11 @@
     , mapKeys
     , modify
     , modifyDef
+    , map
+    , filterWithKey
     ) where
 
-import Prelude hiding (lookup)
+import Prelude hiding (lookup, map)
 import Data.Maybe (fromMaybe)
 import Data.Monoid
 import Data.Foldable (Foldable)
@@ -41,7 +45,7 @@
 import Data.Typeable (Typeable)
 
 #if MIN_VERSION_base(4,7,0)
-import GHC.Exts (IsList(..))
+import qualified GHC.Exts as Exts
 #endif
 
 import Control.DeepSeq
@@ -101,7 +105,7 @@
     {-# INLINE unpack #-}
 
 #if MIN_VERSION_base(4,7,0)
-instance (Eq k, Hashable k, Monoid a) => IsList (MonoidalHashMap k a) where
+instance (Eq k, Hashable k, Monoid a) => Exts.IsList (MonoidalHashMap k a) where
     type Item (MonoidalHashMap k a) = (k, a)
     fromList = MM . M.fromListWith mappend
     {-# INLINE fromList #-}
@@ -160,6 +164,18 @@
 keys = M.keys . unpack
 {-# INLINE keys #-}
 
+-- | /O(n*log n)/. Construct a map with the supplied mappings. If the list
+-- contains duplicate mappings, the later mappings take precedence.
+fromList :: (Eq k, Hashable k) => [(k,a)] -> MonoidalHashMap k a
+fromList = pack . M.fromList
+{-# INLINE fromList #-}
+
+-- | /O(n*log n)/. Construct a map with the supplied mappings. If the list
+-- contains duplicate mappings, the later mappings take precedence.
+toList :: MonoidalHashMap k a -> [(k,a)]
+toList = M.toList . unpack
+{-# INLINE toList #-}
+
 -- | /O(log n)/. Modify a value on some key with a function, if value
 -- under key doesn't exist -- use mempty.
 modify :: (Monoid a, Hashable k, Eq k)
@@ -184,8 +200,19 @@
 
 -- | /O(n)/. Map a function to each key of a map
 mapKeys :: (Monoid a, Hashable k, Eq k, Hashable k', Eq k')
-        => (k -> k') -> MonoidalHashMap k a
-        -> MonoidalHashMap k' a
+        => (k -> k') -> MonoidalHashMap k a -> MonoidalHashMap k' a
 mapKeys f = fromList
-          . map (\(k, v) -> (f k, v))
+          . fmap (\(k, v) -> (f k, v))
           . toList
+{-# INLINE mapKeys #-}
+
+-- | /O(n)/ Filter this map by retaining only elements satisfying a
+-- predicate.
+filterWithKey :: (k -> v -> Bool) -> MonoidalHashMap k v -> MonoidalHashMap k v
+filterWithKey pred = pack . M.filterWithKey pred . unpack
+{-# INLINE filterWithKey #-}
+
+-- | /O(n)/ Transform this map by applying a function to every value.
+map :: (v1 -> v2) -> MonoidalHashMap k v1 -> MonoidalHashMap k v2
+map f = pack . M.map f . unpack
+{-# INLINE map #-}
diff --git a/src/Data/Map/Monoidal.hs b/src/Data/Map/Monoidal.hs
--- a/src/Data/Map/Monoidal.hs
+++ b/src/Data/Map/Monoidal.hs
@@ -12,7 +12,7 @@
 --
 -- While some functions mirroring those of 'Data.Map' are provided
 -- here for convenience, more specialized needs will likely want to use
--- either the @Newtype@ or @Wrapped@ instances to manipulate the
+-- either the 'Newtype' or 'Wrapped' instances to manipulate the
 -- underlying 'Map'.
 
 module Data.Map.Monoidal
@@ -23,6 +23,7 @@
     , member
     , notMember
     , findWithDefault
+    , assocs
     , elems
     , keys
     ) where
@@ -141,6 +142,11 @@
 delete :: Ord k => k -> MonoidalMap k a -> MonoidalMap k a
 delete k = _Wrapping' MM %~ M.delete k
 {-# INLINE delete #-}
+
+-- | /O(n)/. Return all elements of the map and their keys
+assocs :: MonoidalMap k a -> [(k,a)]
+assocs = M.assocs . unpack
+{-# INLINE assocs #-}
 
 -- | /O(n)/. Return all elements of the map in the ascending order of their
 -- keys. Subject to list fusion.