van der Waals heterostructures, composed of vertically stacked inorganic 2D materials, represent an ideal platform to demonstrate novel device architectures and to fabricate on-demand materials. The incorporation of organic molecules within these systems holds an immense potential, since, while nature offers a finite number of 2D materials, an almost unlimited variety of molecules can be designed and synthesized with predictable functionalities. The possibilities offered by systems in which continuous molecular layers are interfaced with inorganic 2D materials to form hybrid organic/inorganic van der Waals heterostructures are emphasized. Similar to their inorganic counterpart, the hybrid structures have been exploited to put forward novel device architectures, such as antiambipolar transistors and barristors. Moreover, specific molecular groups can be employed to modify intrinsic properties and confer new capabilities to 2D materials. In particular, it is highlighted how molecular self-assembly at the surface of 2D materials can be mastered to achieve precise control over position and density of (molecular) functional groups, paving the way for a new class of hybrid functional materials whose final properties can be selected by careful molecular design.