I survey a number of views about how we can obtain knowledge of modal propositions, propositions about necessity and possibility. One major approach is that whether a proposition or state of affairs is conceivable tells us something about whether it is possible. I examine two quite different positions that fall under this rubric, those of Yablo and Chalmers. One problem for this approach is the existence of necessary a posteriori truths and I deal with some of the ways in which these authors respond to the problem, including the use of two-dimensional modal semantics. Conventionalism about modality offers a complementary approach to modal epistemology, prompting us to identify our knowledge of modal truths with our mastery of linguistic or conceptual conventions. Finally, I discuss an approach to modal epistemology deriving from David Lewis's work that seeks to identify structural features of the modal space over which necessity and possibility are defined.