This will be a survey of definitions and questions: Topological Hochschild Homology is the result of applying the classical construction of Hochschild Homology to rings in the category of S-modules. Topological algebraic geometry is the result of applyin classical algebraic geometry to sheaves of sites built from S-modules. Given time, we may compare these ideas to those of Algebro-geometric Topology, which seeks to find the category of S-modules inside a category of sheaves on classical sites.