Cognitive spectrum access (CSA) in in-band D2D-enabled cellular networks is a potential feature that can promote efficient resource utilization and interference management among coexisting cellular and D2D users. In this article, we first outline the challenges in resource allocation posed by the coexistence of cellular and D2D users. Next, we provide a qualitative overview of the existing resource allocation and interference management policies for in-band D2D-enabled cellular networks. We then demonstrate how cognition along with limited information exchange between D2D users and the core network can be used to mitigate interference and enhance spectral efficiency of both cellular and D2D users. In particular, we propose a CSA scheme that exploits channel sensing and interference- aware decision making at the D2D terminals. This CSA scheme at the D2D terminals is complemented by a D2D-aware channel access method at the cellular BSs. The performance gains of the proposed CSA scheme are characterized in terms of channel access probability for a typical D2D transmitter and spectral efficiencies for both cellular and D2D transmissions. Finally, potential research issues that require further investigation are highlighted.