Numerous communication networks are emerging to serve the various demands and improve the quality of service. Heterogeneous users have different requirements on quality metrics such as delay and service efficiency. Besides, the networks are equipped with different types and amounts of resources, and how to efficiently optimize the usage of such limited resources to serve more users is the key issue for communication networks. One powerful mathematical optimization mechanism to solve the above issue is column generation (CG), which can deal with the optimization problems with complicating constraints and block angular structures. In this paper, we first review the preliminaries of CG. Further, the branch-and-price (BP) algorithm is elaborated, which is designed by embedding CG into the branch-and-bound scheme to efficiently obtain the optimal solution. The applications of CG and BP in various communication networks are then provided, such as space-air-ground networks and device-to-device networks. In short, our goal is to help readers refine the applications of the CG optimization tool in terms of problem formulation and solution. We also discuss the possible challenges and prospective directions when applying CG in the communication networks.