Dynamic Programming (DP) is an algorithmic optimization technique that solves complex problems by breaking them into overlapping subproblems, storing their solutions to avoid redundant computation. Developed by Richard Bellman in the 1950s, DP applies to problems exhibiting optimal substructure (where optimal solutions contain optimal sub-solutions) and overlapping subproblems (where the same smaller problems recur multiple times). The key insight is that memoization or tabulation transforms exponential-time recursive algorithms into polynomial-time solutions by trading computation for memory — storing intermediate results in a cache or table rather than recalculating them repeatedly. Understanding when and how to apply DP, and recognizing its patterns across knapsack variants, string algorithms, grid traversals, and tree problems, is essential for solving optimization challenges efficiently.