This chapter establishes 3-polygraphs as a notion of presentation for 2-categories. As expected, those consist in generators for 0-, 1- and 2-dimensional cells, together with relations between freely generated 2-cells, which are represented by generating 3-cells. Any 3-polygraph induces an abstract rewriting system, so that all associated general rewriting concepts make sense in this setting: confluence, termination, etc. However, more specific tools have to be adapted to this context: the notion of critical branching is defined here for 3-polygraphs, along with the proof that confluence of critical branchings implies the local confluence of the polygraph. In the case where the polygraph is terminating, local confluence implies confluence, providing a systematic method to show the convergence of a 3-polygraph. When this is the case, normal forms give canonical representatives for 2-cells modulo the congruence generated by 3-cells, and it is explained how to exploit this to show that a given 3-polygraph is a presentation of a given 2-category.