Consider a finite group G generated by a set of (linear) reflections in Euclidean space. Such groups can be classified by considering them as symmetries of either a polygon or of some root system. However, we can also associate to such a (linear) reflection group a certain simplicial complex, on which G acts as the group of automorphisms. We are then led to consider more general simplicial complexes and their automorphisms. Such are called Coxeter complexes when the group in question admits a particular presentation. This talk will explain Coxeter groups and their complexes, show how they are related to combinatorial geometries, and how we can generalize this interplay between groups and combinatorial geometry with the notion of a building.