Topological Data Analysis (TDA) is a new and fast-growing branch of math, addressing the need for extracting information from big data sets. One of the methods of TDA is persistence theory, which has proven to be very informative. The standard way to approach persistence theory is using persistent homology. In this seminar, I present a different approach, based on the study of tame parametrised chain complexes. This choice is indeed useful, since, firstly, the study of tame parametrised chain complexes includes the one of persistent homology, and thus is more general. Secondly, there are many powerful theoretical tools available in this setting, and such tools allow us to retrieve invariants, and therefore information, in more general cases. I will provide a quick introduction to these theoretical tools, namely to model category theory, and then focus on some examples to explain in details the constructions and the invariants."