I argue that we have good reason for being realist about quantum states. Though a research programme of attempting to construct a plausible theory that accounts for quantum phenomena without ontic quantum states is well-motivated, that research programme is confronted by considerable obstacles. Two theorems are considered that place restrictions on a theory of that sort: a theorem due to Barrett, Cavalcanti, Lal, and Maroney, and an extension, by the author, of the Pusey-Barrett-Rudolph theorem, that employs an assumption weaker than their Cartesian Product Assumption. These theorems have assumptions, of course. If there were powerful evidence against the conclusion that quantum states correspond to something in physical reality, it might be reasonable to reject these assumptions. But the situation we find ourselves in is the opposite: there is no evidence at all supporting irrealism about quantum states.