Software-defined networking (SDN) is a novel network paradigm that enables flexible management for networks. As the network size increases, the single centralized controller cannot meet the increasing demand for flow processing. Thus, the promising solution for SDN with large-scale networks is the multi-controller. In this paper, we present a compressive survey for multi-controller research in SDN. First, we introduce the overview of multi-controller, including the origin of multi-controller and its challenges. Then, we classify multi-controller research into four aspects (scalability, consistency, reliability, and load balancing) depending on the process of implementing the multi-controller. Finally, we propose some relevant research issues to deal with in the future and conclude the multi-controller research.