Heaps and Priority Queues allow data to be accessed in an order. Binary heaps are great, but don't support merging (unions). Binomial heaps solve that problem. Dijkstra and Prim's algorithm can benefit greatly from using a decrease key operation that runs in O(1) time. Fibonacci heaps provide that, while keeping the extract min operation to O(log n) time. Amortized analysis can be used for both.