Device-to-Device (D2D) communication was initially proposed in cellular networks as a new paradigm to enhance network performance. The emergence of new applications such as content distribution and location-aware advertisement introduced new use-cases for D2D communications in cellular networks. The initial studies showed that D2D communication has advantages such as increased spectral efficiency and reduced communication delay. However, this communication mode introduces complications in terms of interference control overhead and protocols that are still open research problems. The feasibility of D2D communications in LTE-A is being studied by academia, industry, and the standardization bodies. To date, there are more than 100 papers available on D2D communications in cellular networks and, there is no survey on this field. In this article, we provide a taxonomy based on the D2D communicating spectrum and review the available literature extensively under the proposed taxonomy. Moreover, we provide new insights to the over-explored and under-explored areas which lead us to identify open research problems of D2D communication in cellular networks.