This article presents an in-depth look at the different aspects of anticipation and describes two intelligent agents which are able to learn human behaviour, to anticipate next actions and then act accordingly. The first agent is intended to predict and to anticipate, with good accuracy, evolutive (indeed adaptive) observed behaviour of a game player. The second is an adaptive interface agent for a particular Web-based application. It is an active browser, interactively assisting and guiding the user by proposing navigation methods.