Combining materials with diverse properties into two‐dimensional (2D) van der Waals heterostructures lies at the heart of electronic, optoelectronic, and photonic applications. Prerequisite is a significant degree of electronic or photonic coupling of the constituents across the heterointerface. Understanding and controlling these interactions is mandatory to achieve the desired functionality. This review focuses on the charge and energy transfer processes and their dynamics in a specific class of van der Waals heterostructures, namely such composed of semiconducting transition metal dichalcogenides and conjugated organic molecules. With the help of prototypical material combinations, the importance of a precise knowledge of the interfacial electronic structure is demonstrated as it governs the excited‐state dynamics. This review aims at providing basic design guidelines to achieve functional 2D organic/inorganic van der Waals heterostructures with final properties that can be designed by careful selection of the organic component.