The Ornstein-Uhlenbeck (OU) process is a cornerstone in the study of stochastic processes, particularly in modeling phenomena that exhibit a tendency to revert towards a long-term mean. Originally developed to describe the velocity of a Brownian particle under the influence of friction, its applications have broadened significantly, spanning fields such as finance (modeling interest rates and commodity prices), biology (describing population dynamics), and signal processing (noise modeling). While the continuous-time OU processOU process is often the initial focus, many real-world observations and computational simulations naturally occur in discrete time steps. This chapter delves into the discrete-time counterpart of the OU processOU process, exploring its definition, key properties, and illustrating its behavior through examples and realizations.