This paper provides a comprehensive survey of Device-to-Device (D2D) communication in cellular networks, a paradigm introduced to enhance network performance and address new use cases such as content distribution and location-aware advertising. D2D communication allows direct communication between mobile users without involving the Base Station (BS) or core network, offering advantages like increased spectral efficiency and reduced communication delay. However, it also introduces challenges such as interference control and protocol design. The paper categorizes the literature based on the spectrum used for D2D communication, specifically inband and outband D2D, and reviews the existing research under these categories. Inband D2D uses the cellular spectrum, which can be further divided into underlay and overlay. Underlay D2D shares resources with cellular communications, while overlay D2D allocates dedicated resources. Underlay D2D has been extensively studied for improving spectrum efficiency, power efficiency, and system performance under QoS/power constraints. Techniques include interference management, mode selection, resource allocation, and network coding. Overlay D2D, on the other hand, uses dedicated resources, reducing interference but potentially limiting cellular resources. Outband D2D uses unlicensed spectrum, eliminating interference issues but requiring coordination between radio interfaces. This category includes controlled and autonomous D2D, where the cellular network manages the second interface or users manage it themselves. Controlled outband D2D is managed by the cellular network, while autonomous outband D2D operates independently. The paper also discusses the contributions of 3GPP's ProSe (Proximity Services) and the challenges and potential research directions in D2D communications. It concludes by summarizing the achievements and open issues in the field, emphasizing the need for advanced mathematical techniques and realistic evaluation scenarios to further advance D2D communication in cellular networks.This paper provides a comprehensive survey of Device-to-Device (D2D) communication in cellular networks, a paradigm introduced to enhance network performance and address new use cases such as content distribution and location-aware advertising. D2D communication allows direct communication between mobile users without involving the Base Station (BS) or core network, offering advantages like increased spectral efficiency and reduced communication delay. However, it also introduces challenges such as interference control and protocol design. The paper categorizes the literature based on the spectrum used for D2D communication, specifically inband and outband D2D, and reviews the existing research under these categories. Inband D2D uses the cellular spectrum, which can be further divided into underlay and overlay. Underlay D2D shares resources with cellular communications, while overlay D2D allocates dedicated resources. Underlay D2D has been extensively studied for improving spectrum efficiency, power efficiency, and system performance under QoS/power constraints. Techniques include interference management, mode selection, resource allocation, and network coding. Overlay D2D, on the other hand, uses dedicated resources, reducing interference but potentially limiting cellular resources. Outband D2D uses unlicensed spectrum, eliminating interference issues but requiring coordination between radio interfaces. This category includes controlled and autonomous D2D, where the cellular network manages the second interface or users manage it themselves. Controlled outband D2D is managed by the cellular network, while autonomous outband D2D operates independently. The paper also discusses the contributions of 3GPP's ProSe (Proximity Services) and the challenges and potential research directions in D2D communications. It concludes by summarizing the achievements and open issues in the field, emphasizing the need for advanced mathematical techniques and realistic evaluation scenarios to further advance D2D communication in cellular networks.