This chapter presents a description of discrete-time systems in the complex frequency domain, together with well-known techniques from the domain of digital signal processing. More specifically, the fundamental concept of the transfer function is defined, and the equivalence between this function and the difference equation that describes the system is discussed and presented via illustrative examples based on the use of a Z transform. The concepts of stability and the causality of discrete-time systems are introduced, together with the very important classes of minimum and maximum phase systems. Then the focus is shifted to the interconnection of such simple systems to create more complex higher-order systems as well as to the concept of the inverse system. A description of discrete-time systems in the state space is then presented, together with the associated methods, including the solution of dynamic equations the connection that exists between the transfer function and these equations. In the last part of the chapter, well-known digital processing techniques are presented in detail at theoretical and practical levels, including the analog-to-digital conversion process via sampling and quantization and techniques of multirate signal processing, such as oversampling, undersampling, and polyphase analysis.