Fifth-generation mobile communication networks (5G)/Beyond 5G (B5G) can achieve higher data rates, more significant connectivity, and lower latency to provide various mobile computing service categories, of which enhanced mobile broadband (eMBB), massive machine-type communications (mMTC), and ultra-reliable and low latency communications (URLLC) are the three extreme cases. A symmetrically balanced mechanism must be considered in advance to fit the different requirements of such a wide variety of service categories and ensure that the limited resource capacity has been properly allocated. Therefore, a new network service architecture with higher flexibility, dispatchability, and symmetrical adaptivity is demanded. The cloud native architecture that enables service providers to build and run scalable applications/services is highly favored in such a setting, while a symmetrical resource allocation is still preserved. The microservice function in the cloud native architecture can further accelerate the development of various services in a 5G/B5G mobile wireless network. In addition, each microservice part can handle a dedicated service, making overall network management easier. There have been many research and development efforts in the recent literature on topics pertinent to cloud native, such as containerized provisioning, network slicing, and automation. However, there are still some problems and challenges ahead to be addressed. Among them, optimizing resource management for the best performance is fundamentally crucial given the challenge that the resource distribution in the cloud native architecture may need more symmetry. Thus, this paper will survey cloud native mobile computing, focusing on resource management issues of network slicing and containerization.