A quantum well solar cell is a special multiple-band gap device with intermediate properties between heterojunction cells (sum of the currents generated in the different materials but voltage controlled by the lowest of the two band gaps) and tandem cells (sum of the voltages but current determined by the worst of the two sub-cells). Strain-balanced GaAsP/InGaAs multi-quantum wells move the absorption edge of GaAs solar cells closer to the optimum value for single junction cells with no need for any partially relaxed buffer layer to accommodate lattice mismatch between the absorbing layers and the substrate. Covering a large spectral range in a single-junction cell has the benefit that the cell remains close to optimal efficiency in the varying spectral conditions of a typical terrestrial concentrator. Though monolithic multi-junction cells have significantly higher efficiency, the series-current constraint means that some of this advantage is lost as the illuminating spectra and the cell temperature change from the values at which the tandem was optimised. The good material quality which can be achieved with these structures makes the cell dark current at the typical operating conditions expected under moderate sunlight concentration (similar to 200x), increasingly dominated by radiative processes the deeper the quantum wells. We will report on high concentration measurements of strain-balanced quantum well solar cells with and without Bragg-stack reflectors and discuss the "additivity" between the short-circuit current and the dark-current. We discuss a 50 shallow well cell with measured AM1.5d efficiency of (26 +/- 1)% at around 200 x concentration. This is approximately 2% higher than a comparable p-n cell with comparable material quality. The good material quality is also responsible for another effect previously observed in single quantum wells becoming measurable in structures with 5 and 10 wells, that is the suppression of carrier recombination in quantum wells with respect to expectations assuming that the quasi-Fermi level separation in the depletion region is equal to the cell output voltage throughout the active region. The latest results are presented together with possible explanations for this effect both in the dark and under illumination. Finally a brief discussion about the potential applications of quantum well solar cells completes the paper.