Supporting ever‐increasing number of mobile users with data‐hungry applications, running on battery‐limited devices, is a daunting challenge for the telecommunication community. Device‐to‐device (D2D) communication, which allows physically proximate mobile users to directly communicate with each other by reusing the spectrum, without going through the base station, holds promise to help us tackle this challenge. In a cellular network, D2D communication offers opportunities for spectrum reuse and spatial diversity that may lead to enhanced coverage, higher throughput, and robust communication in the network. Further, for applications such as weather forecasting and live streaming, which may require the same chunks of data distributed to geographically proximate users, D2D multicasting may provide better utilization of network resources compared to D2D unicast or the base station‐based multicast, such as LTE eMBMS. However, extensive deployment of D2D multicast in a network may introduce various issues, such as severe co‐channel interference due to spectrum reuse, underutilization of spectrum, and rapid battery depletion of the multicasting D2D nodes due to higher transmit power to mitigate co‐channel interference and facilitating data‐relaying. Therefore, this article discusses some of the challenges in supporting D2D multicast communication in cellular networks. It then surveys various existing approaches to address these challenges, which along with some future research directions may help us develop practical D2D multicast protocols for cellular networks.