With increasing dependency on communication systems, finite communication bandwidth has become the bottleneck of networked control system (NCS). Research on NCS is not only concerned about control system but also communication networks. Control and scheduling co-design is a feasible way to solve this bottleneck problem in NCS which aims to ensure both quality of performance (QoP) and quality of service (QoS). For the purpose of better understanding of co-design, we summarize the current results from different perspectives and offer some prospects for future research.