diff --git a/src/binarytree.jl b/src/binarytree.jl
index d5b40da..6e0c240 100644
--- a/src/binarytree.jl
+++ b/src/binarytree.jl
@@ -143,3 +143,89 @@ function _printkeyvalue(io::IO, node::BinaryNode)
     show(ioctx, val)
   end
 end
+
+# -----------
+#  UTILITIES
+# -----------
+
+"""
+  BinaryTrees.minnode(tree)
+
+Find the node with the smallest key in the `tree`.
+
+  BinaryTrees.minnode(node)
+
+Find the node with the smallest key in the subtree rooted at `node`.
+If `nothing` is provided, `nothing` is returned.
+"""
+minnode(tree::BinaryTree) = minnode(root(tree))
+
+function minnode(node::BinaryNode)
+  leftnode = left(node)
+  isnothing(leftnode) ? node : minnode(leftnode)
+end
+
+minnode(node::Nothing) = nothing
+
+"""
+  BinaryTrees.maxnode(tree)
+
+Find the node with the maximum key in the `tree`.
+
+  BinaryTrees.maxnode(node)
+
+Find the node with the maximum key in the subtree rooted at `node`.
+If `nothing` is provided, `nothing` is returned.
+"""
+maxnode(tree::BinaryTree) = maxnode(root(tree))
+
+function maxnode(node::BinaryNode)
+  rightnode = right(node)
+  isnothing(rightnode) ? node : maxnode(rightnode)
+end
+
+maxnode(node::Nothing) = nothing
+
+"""
+  BinaryTrees.prevnext(tree, k)
+
+Returns a tuple of each node immediately before
+and after the `tree` node with key `k`.
+
+If an adjacent node does not exist, `nothing` is returned in its place.
+If `k` is `nothing`, returns `(nothing, nothing)`.
+"""
+function prevnext(tree::BinaryTree, k)
+  prev, next = nothing, nothing
+  current = root(tree)
+  # traverse from the root to the target node, updating candidates
+  while !isnothing(current) && key(current) != k
+    if k < key(current)
+      # current is a potential next (successor)
+      next = current
+      current = left(current)
+    else # k > key(current)
+      # current is a potential previous (predecessor)
+      prev = current
+      current = right(current)
+    end
+  end
+
+  # if the node wasn't found, return the best candidate values
+  if isnothing(current)
+    return (prev, next)
+  end
+
+  # if there is a left subtree, the true previous (predecessor) is the maximum in that subtree
+  if !isnothing(left(current))
+    prev = maxnode(left(current))
+  end
+  # similarly, if there is a right subtree, the true next (successor) is the minimum in that subtree
+  if !isnothing(right(current))
+    next = minnode(right(current))
+  end
+
+  (prev, next)
+end
+
+prevnext(tree::BinaryTree, k::Nothing) = (nothing, nothing)
diff --git a/test/runtests.jl b/test/runtests.jl
index fc18830..4732f6b 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -93,7 +93,7 @@ const BT = BinaryTrees
     BT.insert!(tree, 2, 20)
     BT.insert!(tree, 1, 10)
     BT.insert!(tree, 3, 30)
-    # deleting a key that does not exist 
+    # deleting a key that does not exist
     # does not change the tree
     BT.delete!(tree, 4)
     @test tree === tree
@@ -219,11 +219,32 @@ const BT = BinaryTrees
     @test BT.value(BT.search(tree, (0, 0, 1))) == 1
     @test BT.value(BT.search(tree, (1, 0, 0))) == 3
 
+    # traversal algorithms
+    tree = AVLTree{Int,Float64}()
+    BT.insert!(tree, 0, 5)
+    BT.insert!(tree, 1, 6)
+    BT.insert!(tree, 2, 8)
+    BT.insert!(tree, 3, 10)
+    BT.insert!(tree, 4, 20)
+    BT.insert!(tree, 5, 30)
+    BT.insert!(tree, 6, 40)
+    @test BT.key(BT.minnode(tree)) == 0
+    @test BT.key(BT.maxnode(tree)) == 6
+    @test BT.prevnext(tree, 0)[1] == nothing
+    @test BT.key.(BT.prevnext(tree, 2)) == (1, 3)
+    @test BT.key.(BT.prevnext(tree, 5)) == (4, 6)
+    @test BT.prevnext(tree, nothing) == (nothing, nothing)
+
     # type stability
     tree = AVLTree{Int,Int}()
     @inferred BT.insert!(tree, 2, 20)
     @inferred BT.insert!(tree, 1, 10)
     @inferred BT.insert!(tree, 3, 30)
+    @inferred Nothing BT.minnode(tree)
+    @inferred Nothing BT.maxnode(tree)
+    @inferred Nothing BT.prevnext(tree, 2)[1]
+    @inferred Nothing BT.prevnext(tree, 2)[2]
+    @inferred BT.prevnext(tree, nothing)
     @inferred Nothing BT.search(tree, 2)
     @inferred Nothing BT.search(tree, 1)
     @inferred Nothing BT.search(tree, 3)
@@ -234,6 +255,11 @@ const BT = BinaryTrees
     @inferred BT.insert!(tree, 2)
     @inferred BT.insert!(tree, 1)
     @inferred BT.insert!(tree, 3)
+    @inferred Nothing BT.minnode(tree)
+    @inferred Nothing BT.maxnode(tree)
+    @inferred Nothing BT.prevnext(tree, 2)[1]
+    @inferred Nothing BT.prevnext(tree, 2)[2]
+    @inferred BT.prevnext(tree, nothing)
     @inferred Nothing BT.search(tree, 2)
     @inferred Nothing BT.search(tree, 1)
     @inferred Nothing BT.search(tree, 3)
@@ -244,6 +270,11 @@ const BT = BinaryTrees
     @inferred BT.insert!(tree, "key2", 2)
     @inferred BT.insert!(tree, "key1", 1)
     @inferred BT.insert!(tree, "key3", 3)
+    @inferred Nothing BT.minnode(tree)
+    @inferred Nothing BT.maxnode(tree)
+    @inferred Nothing BT.prevnext(tree, "key2")[1]
+    @inferred Nothing BT.prevnext(tree, "key2")[2]
+    @inferred BT.prevnext(tree, nothing)
     @inferred Nothing BT.search(tree, "key2")
     @inferred Nothing BT.search(tree, "key1")
     @inferred Nothing BT.search(tree, "key3")
@@ -254,6 +285,11 @@ const BT = BinaryTrees
     @inferred BT.insert!(tree, (0, 1, 0), 2)
     @inferred BT.insert!(tree, (0, 0, 1), 1)
     @inferred BT.insert!(tree, (1, 0, 0), 3)
+    @inferred Nothing BT.minnode(tree)
+    @inferred Nothing BT.maxnode(tree)
+    @inferred Nothing BT.prevnext(tree, (0, 1, 0))[1]
+    @inferred Nothing BT.prevnext(tree, (0, 1, 0))[2]
+    @inferred BT.prevnext(tree, nothing)
     @inferred Nothing BT.search(tree, (0, 1, 0))
     @inferred Nothing BT.search(tree, (0, 0, 1))
     @inferred Nothing BT.search(tree, (1, 0, 0))