In the last years, search-based QBF solvers have become essential for many applications in the formal methods domain. The exploitation of their reasoning efficiency has however been restricted to applications in which a ‘satisfiable/unsatisfiable’ answer or one model of an open quantified Boolean formula suffices as an outcome, whereas applications in which a compact representation of all models is required could not be tackled with QBF solvers so far. In this paper, we describe how computational learning provides a remedy to this problem. Our algorithms employ a search-based QBF solver and learn the set of all models of a given open QBF problem in a CNF (conjunctive normal form), DNF (disjunctive normal form), or CDNF (conjunction of DNFs) representation. We evaluate our approach experimentally using benchmarks from synthesis of finite-state systems from temporal logic and monitor computation.