This chapter is about proving the existence of the so-called folk model category structure on ω-categories, following Lafont, Métayer, and Worytkiewicz. This model category structure is a generalization of a model category structure on Cat whose weak equivalences are the equivalences of categories, a folklore result, hence the name. The analogous result for 2-categories was proved by Lack. The folk model category structure is a model category structure on ω-categories whose weak equivalences are the ω-equivalences and whose cofibrant resolutions are the polygraphic resolutions. It is the natural homotopical framework in which the notion of polygraphic resolutions lives. As convincing evidence of this, Métayer’s polygraphic homology can be expressed as a derived functor with respect to the folk model category structure.