The problem of belief change---how an agent should revise her beliefs upon learning new information---has been an active area of research in both philosophy and artificial intelligence. Many approaches to belief change have been proposed in the literature. Our goal is not to introduce yet another approach, but to examine carefully the rationale underlying the approaches already taken in the literature, and to highlight what we view as methodological problems in the literature. The main message is that to study belief change carefully, we must be quite explicit about the ``ontology'' or scenario underlying the belief change process. This is something that has been missing in previous work, with its focus on postulates. Our analysis shows that we must pay particular attention to two issues which have often been taken for granted: The first is how we model the agent's epistemic state. (Do we use a set of beliefs, or a richer structure, such as an ordering on worlds? And if we use a set of beliefs, in what language are these beliefs are expressed?) The second is the status of observations. (Are observations known to be true, or just believed? In the latter case, how firm is the belief?) For example, we argue that even postulates that have been called ``beyond controversy'' are unreasonable when the agent's beliefs include beliefs about her own epistemic state as well as the external world. Issues of the status of observations arise particularly when we consider iterated belief revision, and we must confront the possibility of revising by $\phi$ and then by $\neg \phi$.