What is a model category?

I will give an informal, example-laden introduction to Quillen model structures and explain their prominence in modern homotopy theory. Attendees will get more out of this talk if they know something about categories and are familiar with at least one of the following three gadgets: (1) topological spaces and homotopies, (2) chain complexes and quasi-isomorphisms, (3) simplicial sets and weak equivalences.