Unprojection theory, initiated by Miles Reid, aims to analyze (and construct) complicated commutative rings in terms of simpler ones. One of the main motivations is applications to explicit birational geometry. In another direction, unprojection theory is also related to the structure of Stanley-Reisner rings of certain important classes of simplicial complexes. The main aim of the talk, which is based on joint work with Janko Boehm (Kaiserslautern), is a discussion of these relations.