WANET (wireless ad hoc network) is expected to be deployed in a wide range of civil and military applications. The communicating nodes in these networks might be distributed randomly and are assumed to have packet-forwarding capability in order to communicate with each other over a shared and limited radio channel. Building such networks usually poses a significant technical challenge because energy supplied by batteries is likely to be a scarce resource, and in some applications energy is entirely non-renewable. There are mainly two fundamental classes of energy-aware broadcast/multicast problem in recent research: the MEB/MEM (minimum energy broadcast/multicast) problem and the MLB/MLM (maximum lifetime broadcast/multicast) problem in wireless ad hoc networks with omni-directional and directional antennas. In order to provide a better understanding of the research challenges of the energy-aware multicast routing, this article presents a systematical investigation of current state-of-the-art algorithms for these two classes of optimization problems. Taxonomy, comparison, and open research issues for each problem are also discussed, with an objective to inspire new research interests in this field.