I shall try to convince the audience not to be shy with functional
equation approaches in enumerative combinatorics. They not only solve
(some) problems, but they often teach us a lot too. The proofs they provide
for a specific problem might be less nice than more combinatorial
proofs. But functional
equation approaches sometimes give a unified description of apparently
distinct problems, and the efforts we make to solve one specific
functional equation often teach us what to do in a more generic
case. The talk will be based on recent examples dealing with very
classical combinatorial objects: lattice paths, maps, permutations.
