Understanding the statistical nature of communication signals and systems requires some basic concepts of random processes, since the signals and systems are probabilistic in nature such that they vary randomly with time. Since communication transceivers involve both analog radio frequency and digital baseband processing, both continuous-time and discrete-time random processes are important. In this chapter, a random process is first defined. Then, the concepts of ensemble averaging and time averaging are considered, including the mean and autocorrelation, with an emphasis on wide-sense stationary random processes. Pairs of random processes are then considered along with their cross-correlation and crosscovariance, leading to complex-valued random processes that describe the complex envelope of bandpass random processes including bandpass communication signals, channels, noise, and interference. The power density spectrum of a random process is introduced, being important for characterizing out-of-band emissions in digitally modulated waveforms, and the Doppler shifting introduced by the mobile radio channel. Since filters are essential functions in a communication transceiver, and the communication channel may be considered a filter, the linear filtering of random processes is considered. The chapter concludes with periodic wide-sense stationary or cyclostationary random processes that describe the complex envelope of digitally modulated bandpass waveforms.