Markov decision processes (MDPs), also called stochastic dynamic programming, were born in the 1960s. MDPs model and solve dynamic decision-making problems with multiple periods under stochastic circumstances. There are three basic branches in MDPs: discrete-time MDPs, continuous-time MDPs, and semi-Markov decision processes. Based on these branches, many generalized MDP models were presented to model various practical problems, such as partially observable MDPs, adaptive MDPs, MDPs in stochastic environments, and MDPs with multiple objectives, constraints, or imprecise parameters. MDPs have been applied in many areas, such as communications, signal processing, artificial intelligence, stochastic scheduling and manufacturing systems, discrete event systems, management, and economics.