Animal models have led to important discoveries in biomedical research; their utility to psychiatry and comparative neuroscience is less clear. Disorders of higher-order brain function, schizophrenia chief among them, have proven exceptionally elusive to model. Schizophrenia researchers are of two minds about the possibility of modeling the schizophrenia phenotype(s) in laboratory animals: at one and the same time they are both pessimistic and pragmatic. That is, they admit the discouraging difficulty of the task, and yet proceed, apparently undeterred, with putative animal models of schizophrenia, as if the criticisms that yield the pessimistic judgments simply do not matter. In this article, we survey the criticisms and evaluate their merits. We then ask: what would it mean to take seriously the claim that modeling schizophrenia in at least some non-human animals - namely, rodents - is doomed, futile, impossible? How would, and how should, schizophrenia research be undertaken were the current animal models rejected as simply inadequate to the task? Our aim is not to disparage sound research into the etiology, symptomatology, and treatment of schizophrenia, but rather to emphasize the scope of the gap between current and optimal research practices. We conclude with recommendations to reinvigorate the quest to understand, prevent, and treat schizophrenia.