Recently, the mobile wireless communication has seen explosive growth in data traffic which might not be supported by the current Fourth Generation (4G) networks. The Fifth Generation (5G) networks will overcome this challenge by exploiting a higher spectrum available in millimeter-wave (mmwave) band to improve network throughput. The integration of the millimeter-wave communication with device-to-device communication can be an enabling 5G scheme in providing bandwidth-intensive proximity-based

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... services such as video sharing, live streaming of data, and socially aware networking. Furthermore, the current cellular network traffic can also be offloaded by the D2D user devices thereby reducing loading at Base Stations (BSs), which would then increase the system capacity. However, the mmwave D2D communication is associated with numerous challenges, which include signal blockages, user mobility, high-computational complexity resource allocation algorithms, and increase in interuser interference for dense D2D user scenario. The paper presents review of existing channel and power allocation approaches and mathematical resource optimization solution techniques. In addition, the paper discusses the challenges hindering the realization of an effective allocation scheme in mmwave D2D communication and gives open research issues for further study.