With drone technology's maturity, drone delivery has recently become a hot spot in both industry and academia. As UAVs still have some drawbacks, such as limited flight range and airspace control, vehicle-UAV combined delivery has great potential development. This work studies five operation modes of the vehicle-UAV combined delivery problem, including vehicle-UAV collaborative delivery, vehicle-UAV parallel delivery, vehicle-supported delivery of UAVs, UAV-supported delivery of vehicles, and hybrid-mode delivery. According to different operation modes' characteristics and scenarios, this work analyzes classical elements in terms of delivery vehicles, road networks, node composition, arc segment constraints, and optimization objectives. We also study the expansion elements, including speed ratio, customer number for one-way drone delivery, and stopping strategy. Methods for solving the vehicle-UAV combined delivery problem are introduced and compared, and common instances for tests are listed. Finally, the work proposes the possible future trends of the vehicle-UAV combined delivery problem.