Moore's seminal paper can be taken as the starting point of Algorithmic Learning Theory. Moore studied the problem of unraveling the inner structure of a (minimum state) deterministic finite automaton (DFA) from its input-output behaviour. In this note we pursue Moore's line of research, studying conditions under which it is possible to compute a grammar and/or an automaton for a given language L from a language class C. It doesn't come as a surprise that such conditions must be quite strong. We improve on the algorithms in some cases where computing the grammar/automaton is possible. We correct some mistakes in the literature and come up with some new results, positive and negative, for (subclasses of) context-free languages.