Critical pairs are a minimal representation of two conflicting transformations of a given structure. Their origin goes back to 1970, when Knuth and Bendix introduced them as a tool for proving local confluence of term rewriting systems. In graph transformation, the first notion of critical pairs was presented in the early 90's by Plump.  Since then, and especially in the last few years, other notions of critical pairs have been presented. In this talk, I will review these various notions, together with their associated results.