Truly interactive dialogue systems need to construct meaning on at least a word-by-word basis. We propose desiderata for incremental semantics for dialogue models and systems, a task not heretofore attempted thoroughly. After laying out the desirable properties we illustrate how they are met by current approaches, comparing two incremental semantic processing frameworks: Dynamic Syntax enriched with Type Theory with Records (DS-TTR) and Robust Minimal Recursion Semantics with incremental processing (RMRS-IP). We conclude these approaches are not significantly different with regards to their semantic representation construction, however their purported role within semantic models and dialogue models is where they diverge.