diff --git a/Data/SortedList.hs b/Data/SortedList.hs
--- a/Data/SortedList.hs
+++ b/Data/SortedList.hs
@@ -29,10 +29,13 @@
   , takeWhile
   , dropWhile
   , span
+    -- ** Filtering
+  , partition
   , filter
+  , filterLT
+  , filterGT
   , filterLE
   , filterGE
-  , partition
     -- * Queries
 #if !MIN_VERSION_base(4,8,0)
   , null
@@ -45,10 +48,13 @@
     -- * Unfolding
   , unfoldr
     -- * Others
-  , nub
 #if MIN_VERSION_base(4,6,0)
   , reverse, reverseDown
 #endif
+    -- * Set operations
+  , nub
+  , intersect
+  , union
   ) where
 
 import Prelude hiding
@@ -64,7 +70,7 @@
 import Control.DeepSeq (NFData (..))
 import Data.Foldable (Foldable (..))
 --
-#if MIN_VERSION_base(4,5,0)
+#if MIN_VERSION_base(4,5,0) && !MIN_VERSION_base(4,9,0)
 import Data.Monoid ((<>))
 #endif
 --
@@ -80,9 +86,13 @@
 import Data.Monoid (Monoid (..))
 #endif
 --
+#if MIN_VERSION_base(4,9,0)
+import Data.Semigroup (Semigroup (..))
+#endif
 
 -- | Type of sorted lists. Any (non-bottom) value of this type
---   is a sorted list.
+--   is a sorted list. Use the 'Monoid' instance to append sorted
+--   lists.
 newtype SortedList a = SortedList [a] deriving (Eq, Ord)
 
 instance Show a => Show (SortedList a) where
@@ -123,6 +133,8 @@
 fromSortedList :: SortedList a -> [a]
 fromSortedList (SortedList xs) = xs
 
+-- | Merge two sorted lists. This assumes that both input lists
+--   are sorted.
 mergeSortedLists :: Ord a => [a] -> [a] -> [a]
 mergeSortedLists xs [] = xs
 mergeSortedLists [] ys = ys
@@ -131,9 +143,17 @@
      then x : mergeSortedLists xs (y:ys)
      else y : mergeSortedLists (x:xs) ys
 
+#if MIN_VERSION_base(4,9,0)
+instance Ord a => Semigroup (SortedList a) where
+  SortedList xs <> SortedList ys = SortedList $ mergeSortedLists xs ys
 instance Ord a => Monoid (SortedList a) where
   mempty = SortedList []
+  mappend = (<>)
+#else
+instance Ord a => Monoid (SortedList a) where
+  mempty = SortedList []
   mappend (SortedList xs) (SortedList ys) = SortedList $ mergeSortedLists xs ys
+#endif
 
 -- | /O(1)/. Create a sorted list with only one element.
 singleton :: a -> SortedList a
@@ -226,6 +246,20 @@
 filter :: (a -> Bool) -> SortedList a -> SortedList a
 filter f = fst . partition f
 
+-- | /O(n)/. Select only elements that are strictly less than the argument.
+filterLT :: Ord a => a -> SortedList a -> SortedList a
+filterLT a (SortedList l) = SortedList $ go l
+  where
+    go (x:xs) = if x < a then x : go xs else []
+    go [] = []
+
+-- | /O(n)/. Select only elements that are strictly greater than the argument.
+filterGT :: Ord a => a -> SortedList a -> SortedList a
+filterGT a (SortedList l) = SortedList $ go l
+  where
+    go (x:xs) = if a < x then x : xs else go xs
+    go [] = []
+
 -- | /O(n)/. Select only elements less or equal to the argument.
 filterLE :: Ord a => a -> SortedList a -> SortedList a
 filterLE a (SortedList l) = SortedList $ go l
@@ -354,6 +388,26 @@
 dropWhile :: (a -> Bool) -> SortedList a -> SortedList a
 dropWhile f = snd . span f
 
--- | Return the indices of all elements in a sorted list that satisfy the given condition.
+-- | /O(n)/. Return the indices of all elements in a sorted list that satisfy the given condition.
 findIndices :: (a -> Bool) -> SortedList a -> SortedList Int
 findIndices f (SortedList xs) = SortedList $ List.findIndices f xs
+
+-- | /O(n+m)/. Intersection of sorted lists. If the first list contains duplicates, so will the result.
+intersect :: Ord a => SortedList a -> SortedList a -> SortedList a
+intersect xs ys =
+  let SortedList xs' = xs
+      SortedList ys' = nub ys
+      go [] _  = []
+      go _  [] = []
+      go pp@(p:ps) qq@(q:qs) =
+        case p `compare` q of
+          LT ->     go ps qq
+          EQ -> p : go ps qq
+          GT ->     go pp qs
+  in  SortedList $ go xs' ys'
+
+-- | Union of sorted lists.
+--   Duplicates, and elements of the first list, are removed from the the second list,
+--   but if the first list contains duplicates, so will the result.
+union :: Ord a => SortedList a -> SortedList a -> SortedList a
+union xs ys = xs `mappend` foldl (flip delete) (nub ys) xs
diff --git a/sorted-list.cabal b/sorted-list.cabal
--- a/sorted-list.cabal
+++ b/sorted-list.cabal
@@ -1,5 +1,5 @@
 name:                sorted-list
-version:             0.2.0.0
+version:             0.2.1.0
 synopsis:            Type-enforced sorted lists and related functions.
 description:         Type-enforced sorted lists and related functions.
                      .