With respect to data structures, Chris Okasaki has done substantial research into adopting classic data structures into a purely functional setting, as many of the standard data structures no longer work when using destructive updates. His book “Purely Functional Data Structures” shows how some structures, like binomial heaps and red/black trees, can be implemented quite well in a functional setting, while other basic structures like arrays and queues must be implemented with more elaborate concepts.
If you’re interested in pursuing this branch of the core algorithms, his book would be an excellent starting point.