The past 20 years have witnessed a renaissance of dye chemistry, moving from traditional colorant research toward functional materials. Different from traditional colorant research, the properties of functional materials are governed extensively by intermolecular interactions, thereby entailing significant limitations to the classical approach based on molecular structure-molecular property (color, emission, redox properties, etc.) relationships for the respective dye molecules. However, as discussed in this Perspective, such an approach can be pursued for dye aggregates, and in many cases already well-tailored dimers are sufficient to understand the influence of supramolecular organization on the functional properties of ground and photoexcited states. Illustrative examples will be given for exciton coupling and charge-transfer coupling and how these properties relate to desirable functions such as fluorescence, symmetry-breaking charge separation, and singlet fission in molecular aggregates. While the progress in this research so far mostly originated from studies on well-defined folded and self-assembled structures composed of only two dye molecules, future work will have to advance toward larger oligomers of specific size and geometry. Furthermore, future experimental studies should be guided to a larger extent by theoretical predictions that may be supported by machine learning algorithms and new concepts from artificial intelligence. Beyond already pursued calculations of potential energy landscapes, we suggest the development of theoretical approaches that identify the most desirable dye aggregate structures for a particular property on functional energy landscapes.