Organic semiconductors are materials that are promising for novel optoelectronic applications, such as more efficient solar cells and LEDs. The optoelectronic response of these materials is dominated by bound electron-hole pairs called excitons, which are often strongly affected by hundreds of possible molecular vibrations. Although quantum theory contains all the ingredients to describe these complex phenomena, in practice it is only possible to solve the corresponding equations in small systems with few vibrations. As a result, it has been common to assume weak exciton-vibration interactions and to employ perturbative approaches. Similarly, exciton-photon interactions have almost universally been treated in the so-called weak coupling regime. However, in recent years it has become increasingly clear that these approximations can break down in organic semiconductors, placing an important roadblock towards the novel energy-harvesting technologies that could be based on these materials.

In this thesis we address this issue by developing methods to treat exciton-photon and exciton-vibration interactions, without relying on any approximation regarding their magnitude. We propose a first principles description of hybrid exciton-light (polariton) states that result from strong exciton-photon interactions. We discuss a method to treat strong exciton-vibration interactions, showing that the spatial extent of exciton states controls their magnitude. Subsequently, we present a beyond Born-Oppenheimer method based on tensor networks to study real-time exciton dynamics. By using these methods, we show how selective excitation of vibrational modes can enhance charge transfer. Moreover, through rigorous comparison to experiments, we highlight that tensor network methods are highly accurate, and we generate a `movie' of the photophysical process of singlet fission, which occurs during early light-harvesting by organic molecules and has the potential to increase solar cell efficiencies. Finally, we construct a singlet fission model including the effects of excess energy, vibrations and the solvent of molecules concurrently, demonstrating that the fission mechanism can be qualitatively changed in a controlled manner, allowing for its acceleration by an order of magnitude.