Input-driven models provide an explicit and readily testable account of language learning. Although we share Ellis's view that the statistical structure of the linguistic environment is a crucial and, until recently, relatively neglected variable in language learning, we also recognize that the approach makes three assumptions about cognition and language learning that are not universally shared. The three assumptions concern (a) the language learner as an intuitive statistician, (b) the constraints on what constitute relevant surface cues, and (c) the redescription problem faced by any system that seeks to derive abstract grammatical relations from the frequency of co-occurring surface forms and functions. These are significant assumptions that must be established if input-driven models are to gain wider acceptance. We comment on these issues and briefly describe a distributed, instance-based approach that retains the key features of the input-driven account advocated by Ellis but that also addresses shortcomings of the current approaches.