Software-defined networking (SDN) has recently been all the rage. It has already been successfully applied in many practical fields including campus network, wide area network (WAN) and data centre network. As a next step, SDN is expected to be adopted in cellular networks to deal with some most urgent problems faced by carriers, such as ever soaring capacity demands and differentiated quality of service (QoS)/quality of experience (QoE) requirements introduced by emerging services and a large number of exciting applications. This paper first investigates existing proposals and solutions regarding applying SDN in carrier networks from both industry and academia.Then, as the major contribution of this paper, a novel end-to-end software-defined cellular network (SDCN) architecture, aiming to the evolution towards 5G, is elaborated with adopting several emerging technologies. The proposed SDCN architecture can provide great flexibility, scalability, agility, and efficiency for carriers to keep profit and sustainability. In addition, some crucial issues for implementing each part of the proposed E2E SDCN architecture, i.e., from radio access network (RAN) to backhaul, and finally to core, are thoroughly discussed, respectively.