The Boolean network is an effective tool to characterize dynamic discrete models established on finite sets. However, as the research goes deeper and new demands of some practical issues come into being, traditional Boolean networks fail to model suitably. In this case, Boolean (control) networks with constraints (B(C)NWCs) are proposed. By resorting to semi-tensor product of matrices, the network can be converted equivalently into its algebraic representation, which is convenient to analyze. In this paper, the sources and the types of BNWCs are summarized. Subsequently, the development and status of typical problems including normalization and solvability of BNWCs, are presented. Moreover, some relative results about topological structures of BNWCs are outlined. On the other hand, we pay more attention to controllability of BCNWCs, which are Boolean networks with constraints and inputs. The analysis procedures of controllability in BCNWCs are recommended in term of two categories, which are the Dimitriy-Michael approach and the pre-feedback approach, respectively. Finally, common approaches to design controllable and stabilizable controllers and optimal input signals, the input-state incidence matrix method and the Floyd's algorithm, and some other research orientations such as pinning control and disturbance decoupling, are summarized.