In cognitive science, long-term anticipation, such as when planning to do something next year, is typically seen as a form of ‘higher’ cognition, requiring a different account than the more basic activities that can be understood in terms of responsiveness to ‘affordances,’ i.e. to possibilities for action. Starting from architects that anticipate the possibility to make an architectural installation over the course of many months, in this paper we develop a process-based account of affordances that includes long-term anticipation within its scope. We present a framework in which situations and their affordances unfold, and can be thought of as continuing a history of practices into a current situational activity. In this activity affordances invite skilled participants to act further. Via these invitations one situation develops into the other; an unfolding process that sets up the conditions for its own continuation. Central to our process account of affordances is the idea that engaged individuals can be responsive to the direction of the process to which their actions contribute. Anticipation, at any temporal scale, is then part and parcel of keeping attuned to the movement of the unfolding situations to which an individual contributes. We concretize our account by returning to the example of anticipation observed in architectural practice. This account of anticipation opens the door to considering a wide array of human activities traditionally characterized as ‘higher’ cognition in terms of engaging with affordances.