A point-to-point communication system, in which the transmitter is able to harvest energy from its environment, is considered. Energy harvesting is modeled as the packetized or continuous arrival of the energy throughout the system operation. The design of the optimal offline transmission strategy based on the flow of harvested energy is studied. A systematic approach is proposed in order to maximize the amount of data that can be transmitted under energy harvesting as well as realistic battery constraints. First, a time-varying battery size constraint is considered, which models the degradation of storage capacity over time. Then, a battery that suffers from energy leakage is studied. The optimal transmission scheme is characterized for both models.