Constraint satisfaction is a fundamental artificial intelligence technique offering a simple yet powerful representation. An increasing amount of attention has recently been paid to the development of constraint satisfaction techniques, and it has become clear that the original formulation of a static Constraint Satisfaction Problem (CSP) with hard, imperative constraints is insufficient to model many real problems. Two important extensions to the classical CSP framework which address some of these deficiencies are flexible and dynamic constraint satisfaction. This paper examines in detail classical, flexible and dynamic CSP. It reviews the motivations behind both extensions, and describes the techniques used to solve each type of problem. The paper employs a running example throughout to illustrate the ideas presented.