We show that the class of all circuits is exactly learnable in randomized expected polynomial time using weak subset and weak superset queries. This is a consequence of the following result which we consider to be of independent interest: circuits are exactly learnable in randomized expected polynomial time with equivalence queries and the aid of an NP oracle. We also show that circuits are exactly learnable in deterministic polynomial time with equivalence queries and a Sigma-3 oracle. The paper also contains results on: learning of DNF formulas, learning with membership queries, and an application to Structural Complexity Theory.