The emergence of two new technologies, namely, software defined networking (SDN) and network function virtualization (NFV), have radically changed the development of network functions and the evolution of network architectures. These two technologies bring to mobile operators the promises of reducing costs, enhancing network flexibility and scalability, and shortening the time-to-market of new applications and services. With the advent of SDN and NFV and their offered benefits, the mobile operators are gradually changing the way how they architect their mobile networks to cope with ever-increasing growth of data traffic, massive number of new devices and network accesses, and to pave the way toward the upcoming fifth generation networking. This survey aims at providing a comprehensive survey of state-of-the-art research work, which leverages SDN and NFV into the most recent mobile packet core network architecture, evolved packet core. The research work is categorized into smaller groups according to a proposed four-dimensional taxonomy reflecting the: 1) architectural approach, 2) technology adoption, 3) functional implementation, and 4) deployment strategy. Thereafter, the research work is exhaustively compared based on the proposed taxonomy and some added attributes and criteria. Finally, this survey identifies and discusses some major challenges and open issues, such as scalability and reliability, optimal resource scheduling and allocation, management and orchestration, and network sharing and slicing that raise from the taxonomy and comparison tables that need to be further investigated and explored.