Multimedia multicast/broadcast transmissions provide simultaneous access to a common service to the heterogeneous user equipments (UEs) with different device and channel characteristics. One of the major challenges to the service providers is the exponential growth of energy-constrained UEs. In this context, the optimization of multimedia multicast/broadcast transmissions that consider the constraints imposed by the UEs is a major concern of the service providers to ensure high Quality of Experience levels to the customers with diverse constraints. This paper presents an overview of the multimedia multicast/broadcast challenges and open issues, identifies the main factors and the associated constraints that impact the multimedia transmission, and provides a comprehensive classification, comparison, and analysis of the state-of-the-art user-centric, energyefficient multimedia multicast/broadcast approaches.