A hereditary property of combinatorial structures is a collection of structures (e.g. graphs, words, permutations) which is closed under isomorphism and under taking induced substructures (like induced subgraphs), and contains arbitrarily large structures. Given a property P, we write Pn for the number of distinct (non-isomorphic) structures in P with n elements, and the sequence |Pn| is the speed of P. The speed of words was studied first by Morse and Hedlund in 1938. In the last few years, the ex-Stanley-Wilf conjecture, now Klazar-Marcus-Tardos Theorem was known on the speed of permutations. In this talk I survey that area, pointing out generalizations toward ordered graphs, including few short proofs as well.