Energy harvesting (EH) has recently emerged as a promising technique for green communications, as it can power communication systems with renewable energy. In this paper, we investigate how to adopt cooperative relay selection to improve the short-term performance of EH communication systems. The main focus is on how to efficiently utilize the available side information (SI), including channel side information (CSI) and energy side information (ESI). We formulate relay selection problems with either non-causal or causal SI, with an emphasis on the more practical causal case. For this causal SI case, we propose a low-complexity relay selection strategy based on the relative throughput, that is, in each block, the relay with enough energy and with the highest instantaneous throughput compared with the average throughput is selected. This relay selection rule captures the key characteristic of EH systems, namely, each relay should have some chance to be selected so that the harvested energy can be efficiently utilized, and it should be selected only if its throughput is near its own peak. Simulation results will show that the proposed relay selection method provides significant throughput gain over the conventional one which is only based on the current side information.