Mechanisms for adapting models, filters, decisions, regulators and soon to changing properties of a system or a signal are of fundamental importance in many modern signal processing and control algorithms. In this chapter we give an overview of some basic set-ups and algorithms that are used for this. We pay special attention to the rationale behind the different algorithms, thus distinguishing between "optimal" algorithms and "ad hoc" algorithms. We also give an outline of the basic approaches to performance analysis of adaptive algorithms.