Cooperative communication mechanisms have been proposed as an effective way of exploiting the spatial diversity to improve the quality of wireless transmissions. To the best of our knowledge, a number of research efforts have been paid to study how to employ diversity to the network layer routing design, realizing the minimum energy expenditure in the data transmission. However, there is a lack of a systematic strategy for evaluating the existing schemes. To address this issue, we first develop a taxonomy to summarize the existing energy-efficient cooperative routing algorithms and compare their pros and cons. In particular, we focus on the relay set selection strategies, which have great impact on energy saving. To fairly compare the performance of those schemes, we conduct theoretical analysis and derive three theorems to instruct energy-efficient cooperative routing. Our extensive experiments validate our findings. Our research summarizes the state-of-art research development and lay out future directions in this area.