This chapter introduces all the notions and tools necessary to define and establish the existence of the folk model category structure on ω-categories. Particular focus is placed on the concept of ω-equivalences, which will serve as the weak equivalences of this model structure. The class of ω-equivalences is the appropriate generalization to ω-categories of the class of equivalences of ordinary categories. In particular, an ω-equivalence between 1-categories is nothing but an equivalence of categories. To define this notion, it is necessary to generalize the concept of an invertible cell (or isomorphism). This leads to the notion of a reversible cell, which is, in intuitive terms, a cell admitting an inverse up to cells admitting inverses, up to cells admitting inverses, etc. Another fundamental tool is the ω-category of reversible cylinders in an ω-category, which will lead to a sensible notion of homotopy.