[en] This Topical Review discusses insights into the physical mechanisms of nanostructure solar cell operation as provided by numerical device simulation using a state-of-the-art quantum-kinetic framework based on the non-equilibrium Green’s function formalism. After a brief introduction to the field of nanostructure photovoltaics and an overview of the existing literature on theoretical description and experimental implementation of such devices, the quantum-kinetic formulation of photovoltaic processes is discussed in detail, together with more conventional modeling approaches, such as global detailed balance theory and the semi-classical drift-diffusion-Poisson–Maxwell picture. Application examples provided subsequently include III–V semiconductor nanostructures ranging from ultra-thin absorbers to quantum well and quantum dot solar cell devices. The focus is on common features encountered in photovoltaic nanostructure architectures, such as the impact of configurational parameters and operating conditions on device characteristics, and the pronounced deviations from the semiclassical bulk picture. Ultra-thin absorbers are investigated with focus on the effect of built-in fields and contact configuration on radiative rates and currents. For the case of single and multi-quantum-well p–i–n devices, generation, recombination and escape of carriers are discussed, and quantum well superlattice solar cells are considered with regard to charge carrier transport regimes ranging from band-like transport in miniband states to sequential tunneling between neighboring periods. Double quantum well structures are further studied in the context of tunnel junctions for multi-junction solar cells. The investigation of quantum dots covers the fluorescence of colloidal nanoparticles for luminescent solar concentrators as well as the impact of configurational parameters on the photovoltaic properties of regimented quantum dot arrays, in both single-junction and intermediate-band configurations. (topical review)