State merging algorithms have emerged as the solution of choice for the problem of inferring an unknown regular grammar consistent with a given set of labeled samples, a known NP-hard problem of great importance in the grammatical inference area. These methods derive a small deterministic finite automaton from a set of labeled strings by merging parts of the augmented prefix tree acceptor that corresponds to this set. Experimental and theoretical evidence have shown that the generalization ability exhibited by the resulting automata is highly correlated with the number of states in the final solution. In this talk, we survey existing algorithms that search the tree of possible mergings, and compare their performance in a number of existing benchmarks.