This is the first book-length treatment of the Variational Bayes (VB) approximation in signal processing. It has been written as a self-contained, self-learning guide for academic and industrial research groups in signal processing, data analysis, machineearning, identification and control. It reviews the VB distributional approximation, showing that tractable algorithms for parametric model identification can be generated in off-line and on-line contexts. Many of the principles are first illustrated via sy-to-follow scalar decomposition problems. In later chapters, successful applications are found in factor analysis for medical image sequences, mixture model identification and speech reconstruction. Results with simulated and real data are presented in tail. The unique development of an eight-step "VB method", which can be followed in all cases, enables the reader to develop a VB inference algorithm from the ground up, for their own particular signal or image model.