3D NoC has attracted a lot of attention from both academia and industry with the advantages such as shorter global connection, higher integration density and smaller size. The research on 3D NoCs not only directly affects the development of 3D IC and 3D chip industries but also influences national security. In recent years, 3D NoC has become an important trend in the research of network-on-chip with considerable progress, but many challenges remain. This paper gives a brief introduction of the major issues and reviews the state of arts. It reviews the key problems for the research of 3D NoC in 12 categories including network topology, routing mechanism, performance evaluation, communication fault tolerance, power consumption, mapping, testing, switching technique, QoS, flow control, and resource network interface. It then discusses in detail the research progress and solutions for each type of problems. The problems for network topology include customized topology design for 3D NoC, development of simulation platforms, prototype of 3D NoC based on new topologies and the introduction of wireless. The problems for routing algorithms include new routing algorithm for 3D Torus, new routing algorithms based on the combination of oblivious routing and adaptive routing. The problems for fault tolerance include fault tolerance for permanent errors, adding simulation of the physical link into the original simulation platform, and taking the locality of the communications into consideration. The problems for power consumption include the comprehensive optimization of topology, routing and floorplanning, combination of static and dynamic controls, and power consumption model for 3D NoC with more accuracy. The problems for mapping include balance of heat precipitation, optimization of mapping evaluation model under the dynamic routing strategy, low power mapping algorithms, and mapping combination based on intelligent optimization algorithms. The problems mentioned above all deserve the attention for future research on 3D NoCs.