Recent work in philosophy and semantics has raised challenges to truth-conditional theories of epistemic modals. At the same time, a truth-conditional account has remained the dominant view of counterfactuals (with some exceptions). I argue that the challenges raised for epistemic modals generalize to counterfactuals, and encourage a nonclassical treatment of both. I develop a possibility semantics, building on the possibility modal logics introduced by Lloyd Humberstone in the Eighties and recently revived by Wes Holliday. The new semantics has two philosophical payoffs: it places a new notion of possibility at the center of linguistic theories of modality, and it encourages rethinking what expressivism about modality consists in.