As computer systems are more and more closely integrated into the physical world, real-time systems are required to perform more and more complex computation tasks. The development of multi-core processors makes it possible to fulfill the requirements of both real-time constraints and high computation demands. The research on real-time multicore system has attracted a lot of attention in recent years. This paper presents a survey on the research of real-time multicore system. The survey first introduces the main research problems and challenges. Then, a detailed review is provided covering the various topics, such as shared resource interference, real-time scheduling in multi-core system, parallel real-time software design, multicore virtualization, and power management under real-time constraints. Open issues and research directions are also identified in this survey.