Energy harvesting (EH) has recently emerged as a promising technique for green communications. To realize its potential, communication protocols need to be redesigned to combat the randomness of the harvested energy. In this paper, we investigate how to apply relaying to improve the short-term performance of EH communication systems. With an EH source and a non-EH half-duplex relay, we consider the problem of maximizing the achievable rate for a given time duration. The half-duplex constraint at the relay renders the design problem quite challenging, as the source and relay transmission periods should be carefully scheduled. Moreover, the adaptive power allocation is needed at the source to combat the random energy arrivals. A key finding is that the optimal power allocation algorithm, called directional water-filling (DWF), for the single-hop EH system can serve as guideline for the design of a two-hop communication system, as it not only provides an achievable performance upper bound, but also forms the basis to derive the optimal solution for our design problem. Based on a modified energy profile according to the DWF power allocation, we derive key properties of the optimal solution and thereafter propose an efficient algorithm to maximize the throughput. Simulation results show that both scheduling and power allocation optimizations are necessary in two-hop EH communication systems.