Formal epistemology, or at least the approach to formal epistemology that develops a logic and formal semantics of knowledge and belief in the possible worlds framework, began with Jaakko Hintikka's book Knowledge and Belief, published in 1962. It was later developed and applied to problems in theoretical computer science and game theory, as well as within epistemology. This paper surveys some of these developments, focusing on the formal relations between knowledge and belief, and on the way that the logics of knowledge and belief connect with some traditional problems in epistemology.