The opportunities and flexibility in relay networks and orthogonal frequency-division multiple access (OFDMA) make the combination a suitable candidate network and air-interface technology for providing reliable and ubiquitous high-data-rate coverage in next-generation cellular networks. Advanced and intelligent radio resource management (RRM) schemes are known to be crucial toward harnessing these opportunities in future OFDMA-based relay-enhanced cellular networks. However, it is not very clear how to address the new RRM challenges (such as enabling distributed algorithms, intra-cell/inter-cell routing, intense and dynamic co-channel interference (CCI), and feedback overhead) in such complex environments comprising a plethora of relay stations (RSs) of different functionalities and characteristics. Employment of conventional RRM schemes in such networks will highly be inefficient if not infeasible. The next-generation networks are required to meet the expectations of all wireless users, irrespective of their locations. High-data-rate connectivity, mobility, and reliability, among other features, are examples of these expectations. Therefore, fairness is a critical performance aspect that has to be taken into account in the design of prospective RRM schemes. This paper reviews some of the prominent challenges involved in migrating from the conventional cellular architecture to the relay-based type and discusses how intelligent RRM schemes can exploit the opportunities in relay-enhanced OFDMA-based cellular networks. We identify the role of multiantenna systems and explore the current approaches in literature to extend the conventional schedulers to next-generation relay networks. This paper also highlights the fairness aspect in such networks in the light of the recent literature, provides some example fairness metrics, and compares the performances of some representative algorithms.