Distribution system infrastructures are vulnerable to extreme weather events, such as hurricane, ice coating, flood, and wildfires. Resilience is a measure of the system's ability to prevent the damage during extreme events and to recover the system function after such events. With the economic development, it becomes increasingly important for power utilities to maintain critical loads always in service and to reduce the unserved energy of all loads. If many distribution system equipments are damaged, the utility companies dispatch static or mobile distributed energy resources, reconfigure the network topology in order to restore the islanded sections of the distribution system. In recent years, a large number of studies have been done on operation and planning strategies to enhance the distribution system resilience. This review paper introduces the background of resilient distribution system. Then, it makes a comprehensive summary of the resources for resilience enhancement, the mathematical model of operation and planning algorithms. In particular, the objective function, mathematical formulation, decision variables, and solution algorithm of each study are compared. Finally, the roadmap of resilient distribution system is extracted and the future research direction on this topic is proposed.