A series of decisions should be taken to get the best result. For example, in a treasure hunt game, you should decide step by step a certain path to get the best treasure. The travel has a cost, and the treasure has to overcompensate for it. This kind of problem, of a dynamic nature, is contemplated by dynamic programming and in a different way by Pontryagin’s principle. In particular, the discrete version of dynamic programming is an important algorithm in practical terms. The chapter considers crucial computational aspects and introduces relevant application examples like the knapsack problem, warehouse expansion, genetic sequence alignment, weighted interval scheduling, and management of medical teams. Several programs in MATLAB are included.