Philosophers have on occasion noticed various analogies between interpretive approaches to statistical mechanics and quantum mechanics. Probably the most often noted analogy is between the Boltzmannian approach to statistical mechanics and the de Broglie-Bohm approach to quantum mechanics. The possible and pertinent analogies do not end there however. The purpose of this talk is to draw them out in order to see what is suggested about the two theories' interpretation. The main lessons I draw are as follows. First, I claim that there is at least one interpretation available in statistical mechanics which has been so far overlooked and has a natural analogy in the Everettian interpretation of quantum mechanics. Second, I show that to a certain extent the interpretive choices in both theories depend importantly in how stochasticity is interpreted, a point which has not been seriously raised in the literature. Finally, I suggest that pursuing these analogies suggests the possibility of a kind of “measurement problem” in statistical mechanics.