Harvesting ambient energy from the environment has become an attractive possibility for nodes in wireless networks. In addition to being environmentally friendly, energy harvesting networks promise almost perpetual operation which has been a holy grail for autonomous networks such as wireless sensor networks, and more recently M2M. However, achieving these benefits requires rethinking communication and network algorithms in the presence of energy harvesting. In particular, energy consumption schedules are restricted by arbitrary energy causality constraints. This paper attempts to make a concise survey of the recent body of literature which have defined and solved scheduling and optimization problems, and derived information-theoretic bounds for communication systems with energy harvesting transmitters.