The detriment of global warming caused by greenhouse gases emission involves all aspects of human existence, ranging from natural disasters to biological chain breaks. Cellular networks, especially 5G cellular networks not only provide the key digital infrastructure for promoting the digital information world but also produce massive carbon emission when the energy consumption of 5G cellular networks is increased five to ten times compared with that of 4G. In the construction and maintenance of the next generation cellular networks, it is an inevitable challenge to reduce energy consumption and carbon emission of communication devices, such as base stations, switches and servers. In this article, we first determine terminologies and definitions for carbon emission and carbon efficiency of mobile communication systems. In particular, the carbon emission of current mobile communication systems, as well as the relationship between carbon efficiency, energy efficiency and spectrum efficiency, is elaborated. To achieve the goal of carbon neutrality, we propose a four-layer network architecture assisted by an overall carbon neutral network management module. Finally, we summarize the challenges and enabling technologies to meet the requirements of carbon neutrality for 6G cellular networks.