Adding dilute concentrations of nitrogen (N) or bismuth (Bi) into conventional III-V semiconductor alloys causes a large bowing of the bandgap energy due to the modification of the electronic band structure. This behaviour has attracted significant interest due to the resulting optical and electronic properties. Firstly, the authors present theoretical band structure models for GaAs-based dilute nitride, dilute bismide and dilute bismide-nitride alloys and then use them within current continuity equations to show the photovoltaic behaviour. To describe the band structures of these highly mismatched III-V semiconductor alloys, the authors introduce a 10-, 12- and 14-band k · p Hamiltonian for dilute nitride, dilute bismide and dilute bismide-nitride semiconductors, respectively. The authors then use this approach to analyse GaBiAs multi-quantum well p-i-n structures for photovoltaic performance. Through theoretical analysis the authors can: (i) elucidate important trends in the properties and photovoltaic performance of GaBiAs QW structures and (ii) comment generally on the suitability of GaBiAs alloys and heterostructures for applications in multi-junction solar cells. In particular, the authors identify and quantify the limitations associated with current GaBiAs solar cells, and describe the improvements in performance that can be expected pending further development of this emerging class of devices.