The transport of excitation energy in molecular aggregates is of crucial importance for the function of organic optoelectronic devices and next‐generation solar cells. First, this review summarizes the theoretical background of the nature of the electronically excited states of molecular aggregates. For these systems, the electronic interaction between the monomers leads to the formation of exciton states. This goes along with a shift of the excitation energies and a redistribution of the oscillator strength with respect to the monomers. Next, a brief overview is provided over experimental techniques that allow to study the properties of excitons in molecular aggregates. This includes single‐molecule spectroscopy, coherent two‐dimensional (2D) spectroscopy, and single‐molecule coherent spectroscopy. Finally, examples of molecular aggregates spanning the range from natural systems that act in photosynthesis as light‐harvesting antennas to artificial aggregates built from synthetic chromophores are illustrated.