As heterogeneous networks (HetNets) emerge as one of the most promising developments toward realizing the target specifications of Long Term Evolution (LTE) and LTE-Advanced (LTE-A) networks, radio resource management (RRM) research for such networks has, in recent times, been intensively pursued. Clearly, recent research mainly concentrates on the aspect of interference mitigation. Other RRM aspects, such as radio resource utilization, fairness, complexity, and QoS, have not been given much attention. In this paper, we aim to provide an overview of the key challenges arising from HetNets and highlight their importance. Subsequently, we present a comprehensive survey of the RRM schemes that have been studied in recent years for LTE/LTE-A HetNets, with a particular focus on those for femtocells and relay nodes. Furthermore, we classify these RRM schemes according to their underlying approaches. In addition, these RRM schemes are qualitatively analyzed and compared to each other. We also identify a number of potential research directions for future RRM development. Finally, we discuss the lack of current RRM research and the importance of multi-objective RRM studies. ©2014 IEEE.