Enabling applications that exploit heterogeneous data in the Semantic Web will require us to harness a broad variety of semantics. Considering the role of semantics in a number of research areas in computer science, we organize semantics in three forms — implicit, formal, and powerful — and explore their roles in enabling some of the key capabilities related to the Semantic Web. The central message of this article is that building the Semantic Web purely on description logics will artificially limit its potential, and that we will need to both exploit well-known techniques that support implicit semantics, and develop more powerful semantic techniques.