The future wireless mobile communication demands for the increased transmission rate, spectrum efficiency, and energy efficiency by orders of magnitude, while it also targets at providing much uniform coverage and shorter time delay. Amorphous cellular network, which is based on flexible networking, can fully exploit the wireless resources and significantly enhance user experience, and is then deemed as the most promising research area for the next generation of broadband green communications. Despite of all these advantages, the related research remains in its initial stage, while lots of challenges still reside in the fundamental theory and key technologies which ask for further investigation. The article intends to carry out the analysis of channel characteristic and information theory under the frame of amorphous cellular networks. The transmission technologies of amorphous cellular networks are studied, the comprehensive environment sensing is performed, and dynamic resource allocation is designed. The core theoretical issues are focused on, such as the overlapped coverage of multiple layer cells, the separation of control planes and user planes, as well as the decoupling of up/downlink access mode. We expect to formulate complete communication theory and methodology for amorphous cellular networks, tremendously improve the system throughput and region capacity, achieve the uniform coverage with full dimensionally, and ultimately meet the growing demand of future mobile communication traffic flow with high quality user experience.