Dynamic programming (DP) is useful when a problem can be broken down into smaller, overlapping subproblems and the results of those subproblems can be reused to solve the overall problem. Some indicators that a problem can be solved with DP include recursive solutions that compute the same values multiple times. Problems that involve finding the optimal solution, like shortest paths, knapsack, or sequence alignment, often benefit from DP. The two main types of DP are top-down (using recursion and memoization) and bottom-up (using iteration and a table). Mastering dynamic programming is crucial for solving many optimization problems efficiently.