Device-to-Device (D2D) communication is expected to enable a number of new services and applications in future mobile networks and has attracted significant research interest over the last few years. Remarkably, little attention has been placed on the issue of D2D communication for users belonging to different operators. In this paper, we focus on this aspect for D2D users that belong to different tenants (virtual network operators), assuming virtualized and programmable future 5G wireless networks. Under the assumption of a cross-tenant orchestrator, we show that significant gains can be achieved in terms of network performance by optimizing resource sharing from the different tenants, i.e., slices of the substrate physical network topology. To this end, a sum-rate optimization framework is proposed for optimal sharing of the virtualized resources. Via a wide site of numerical investigations, we prove the efficacy of the proposed solution and the achievable gains compared to legacy approaches.
 Device-to-device (D2D) communications underlaying a cellular infrastructure has recently been proposed as a means of increasing the cellular capacity, improving the user throughput and extending the battery lifetime of user equipments by facilitating the reuse of spectrum resources between D2D and cellular links. In network assisted D2D communications, when two devices are in the proximity of each other, the network can not only help the devices to set the appropriate transmit power and schedule time and frequency resources but also to determine whether communication should take place via the direct D2D link (D2D mode) or via the cellular base station (cellular mode). In this paper we formulate the joint mode selection, scheduling and power control task as an optimization problem that we first solve assuming the availability of a central entity. We also propose a distributed suboptimal joint mode selection and resource allocation scheme that we benchmark with respect to the centralized optimal solution. We find that the distributed scheme performs close to the optimal scheme both in terms of resource efficiency and user fairness. Device-to-device (D2D) communications was initially proposed in cellular networks as a new paradigm for enhancing network performance. The emergence of new applications such as content distribution and location-aware advertisement introduced new user cases for D2D communications in cellular networks. The initial studies showed that D2D communications 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 Long-Term Evolution Advanced is being studied by academia, industry, and standardization bodies. To date, there are more than 100 papers available on D2D communications in cellular networks, but there is no survey on this field. In this paper, 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 into the over-explored and under-explored areas that lead us to identify open research problems of D2D communications in cellular networks.