Colloidal gels: equilibrium and non-equilibrium routes

We attempt a classification of different colloidal gels based on colloid-colloid interactions. We discriminate primarily between non-equilibrium and equilibrium routes to gelation, the former case being slaved to thermodynamic phase separation while the latter is individuated in the framework of competing interactions and of patchy colloids. Emphasis is put on recent numerical simulations of colloidal gelation and their connection to experiments. Finally, we underline typical signatures of different gel types, to be looked at, in more detail, in experiments. (topical review)