Mathematical structures known as algebras serve as part of the theoretical foundation for any field of mathematical research, as well as for related areas like physics and engineering. In the research area known as representation theory of algebras, in which the project “Geometric methods in higher homological algebra” has its origin, the ultimate aim is to understand the underlying structure of such algebras. In particular, given an algebra A, one would like to be able to describe the category modA of finitely generated A-modules. We aim to explain this setup to a general audience and to highlight how so-called geometric models provide a powerful toolbox to study modA. Time permitting, we outline our ongoing work on extending one of these geometric models to a broader and less restrictive framework.