During the last decade, psycholinguists have begun to investigate language comprehension using natural tasks in which the participants have well-defined behavioral goals. The results of these investigations lead to a view of language processing in which linguistic and non-linguistic information are rapidly integrated to dynamically update referential domains, inform parsing decisions, and develop context-specific interpretations. I'll review some of these results, most of which are broadly consistent with the HPSG framework. I'll also outline some challenges for grammatical frameworks that seek to inform processing work, inviting members of the HPSG community to take up these challenges or point the psycholinguistic community to relevant existing work. Some of the easier challenges involve the discourse "meaning" of phrasal and clausal constructions; harder challenges involve the plasticity of the processing system.