This work considers an energy harvesting transmitter that gathers a continuous flow of energy from intermittent sources, thus relaxing the modeling assumption of discrete amounts of harvested energy present in all previous work on energy harvesting communications. Tools from convex analysis are utilized to describe the optimal transmission policy as the boundary of a properly defined region based on the energy profile. The results are extended to include models where the transmitter has a finite capacity battery with various imperfections, as well as those that incorporate a processing cost (circuit power) at the transmitter whenever it is in operation.