Adaptation is the ability of cells, tissues and organisms to rapidly and reversibly modify their properties to maximize fitness in a changing environment. The activity of immune-system components unfolds in the remarkably heterogeneous milieus to which they are exposed in different tissues, during homeostasis or during various acute or chronic pathological states. Therefore, adaptation is essential for immune cells to tune their responses to a large variety of contexts and conditions. The adaptation of immune cells reflects the integration of multiple inputs acting simultaneously or in a temporal sequence, which eventually leads to transcriptional reprogramming and to various functional consequences, some of which extend beyond the duration of the stimulus. A range of adaptive responses have been observed in both adaptive immune cells and innate immune cells; these are referred to with terms such as 'plasticity', 'priming', 'training', 'exhaustion' and 'tolerance', among others, all of which can be useful for defining a certain immunological process or outcome but whose underlying molecular frameworks are often incompletely understood. Here we review and analyze mechanisms of adaptation and memory in immunity with the aim of providing basic concepts that rationalize the properties and molecular bases of these essential processes.