An abundance of evidence (much of it from research at UMD) suggests that sentence comprehension processes respect grammatical constraints in real time. That is, every stage of processing seems to be subject to the same constraints that we see in offline judgments. However, this surface-level similarity does not entail that there is a transparent mapping between the representations or computations invoked at the grammatical and algorithmic levels. For example, in a grammatical theory, a dependency between two elements in a sentence usually exists in multiple levels of representation--syntactic, semantic, and pragmatic. However, processing models focus on how the two elements come to be linked together at all, without necessarily addressing how syntactic, semantic and pragmatic relationships follow. I will discuss three cases where there is a potential mismatch between the distinctions made in the grammar and the processes involved in comprehension: pronoun resolution, WH dependencies, and scalar implicature.