A declarative action model is a compact representation of the state transitions of dynamic systems that generalizes over world objects. The specification of declarative action models is often a complex hand-crafted task. In this paper we formulate declarative action models via state constraints, and present the learning of such models as a combinatorial search. The comprehensive framework presented here allows us to connect the learning of declarative action models to well-known problem solving tasks. In addition, our framework allows us to characterize the existing work in the literature according to four dimensions: (1) the target action models, in terms of the state transitions they define; (2) the available learning examples; (3) the functions used to guide the learning process, and to evaluate the quality of the learned action models; (4) the learning algorithm. Last, the paper lists relevant successful applications of the learning of declarative actions models and discusses some open challenges with the aim of encouraging future research work.