MDPs have been applied in many areas, such as communications, signal processing, artificial intelligence, stochastic scheduling and manufacturing systems, discrete event systems, management and economies. This book examines MDPs and their applications in the optimal control of discrete event systems (DESs), optimal replacement, and optimal allocations in sequential online auctions. The book presents three main topics: a new methodology for MDPs with discounted total reward criterion; transformation of continuous-time MDPs and semi-Markov decision processes into a discrete-time MDPs model, thereby simplifying the application of MDPs; application of MDPs in stochastic environments, which greatly extends the area where MDPs can be applied. Each topic is used to study optimal control problems or other types of problems.