This chapter contains various aspects of ideal and module systems in polynomial domains. We start with a strong version of the Dedekind-Mertens Lemma and discuss several of its applications. Next we review the theory of v- and t-ideals in polynomial domains and discuss the construction of general module systems in polynomial domains. Eventually we close with an elaborate investigation of Nagata rings and Kronecker function rings in the general semistar setting. We highlight the connection with Lorenzen monoids and the helpfulness of the module system approach in this context.