This talk consists of two parts. In the first part, we give an overview of the theory of model categories. This provides a framework which axiomatizes the notion of homotopy which is familiar from the setting of topological spaces. Originally developed by Quillen in the 1960s, these ideas allowed for a formalization of the similarities between homotopy theory and homological algebra. In particular, there are important connections between topological spaces, simplicial sets and chain complexes. We will see that the structure of a model category allows for the construction of a categorical localization at the so-called class of weak equivalences. For example, this can be applied to the model category of chain complexes, giving rise to the derived category of an abelian category. In the second part, we concentrate on the category of simplicial presheaves. In 1987, it was shown by Jardine that the category of simplicial presheaves can be endowed with the structure of a model category. This makes it possible to consider the homotopy theory of presheaves. In recent years, these ideas have received renewed interest, as they can be used in the construction of different flavors of derived geometry. For example, it has been shown that those simplicial presheaves which properly encode a notion of homotopy can be characterized by a descent condition in terms of hypercovers. In turn, this descent condition can be interpreted as a formulation of the classical sheaf axioms 'up to homotopy'.