This paper presents a survey on energy harvesting (EH) wireless communication networks focusing on channel capacity, transmission schemes, and power optimization. While many network researchers focus on energy management policies addressing the intermittency and randomness of the EH processes, but the channel capacity, and transmission power optimization have not been fully explored yet. In this paper, we provide a review and analysis of channel capacity, offline and online transmission schemes, and power optimization from an information theory perspective. By reviewing and analyzing wireless networking literature, we found that EH is a technologically feasible and economically viable paradigm for cost-effectiveness in the design and deployment of next-generation wireless networks. Finally, we identify open research problems and future research directions in the emerging field of EH wireless networks. We expect this study to stimulate more research endeavors to build energy-efficient scalable next-generation wireless network systems.