Since the inception of interactive systems, it has been clearly stated that user interfaces (UIs) need to be adapted to their users in context, adaptation being either engineered at design time or computed at run time. Experience shows that adapting user interfaces dynamically is not risk-free: while there may be expected advantages, they may be outweighed or even prevented by several unfavorable consequences, the primary one coming from the adaptation process itself. There may be a cognitive disturbance that occurs in the user’s mind when the interface changes compared to its original state. This chapter first outlines the adaptation life cycle’s seven stages before discussing some of the challenges in adapting user interfaces generally and adaptive user interfaces specifically. To review the state-of-the-art in UI adaptation, this chapter breaks down the definition of an adaptation operation using the Event-Condition-Action paradigm, qualified by the properties it is expected to satisfy. Thereby, the four parts are the Event that initiates the adaptation, the Condition the adaptation is applicable under, the Adaptation to be applied, and the overall worth of the operation in terms of its quality properties. For each part, we examine and discuss a series of representative works to improve our general understanding of how adaptation works and should be implemented. In the end, it explores a couple of adaptation-related topics that indicate a promising future. A playlist of videos showing adaptive user interfaces is also available to review research and innovation in user interfaces adaptation.