Mergeable Exact Order Statistics Data Structure
Most balanced trees that have logarithmic-time insert and delete also have logarithmic time $merge$. This includes AVL trees, red-black trees, and B trees.

You can see this question on Stack Overflow for several references results. They include a paper on CGAL (red-black), a reference to the OCaml standard library (AVL), as well as the red-black tree chapter of CLRS's Introduction to Algorithms.

When I was learning about this topic, I was happy to find that $merge$ is actually usually a simpler operation than $insert$ and $delete$.