The nanostructuring of silicon surfaces--known as black silicon--is a promising approach to eliminate front-surface reflection in photovoltaic devices without the need for a conventional antireflection coating. This might lead to both an increase in efficiency and a reduction in the manufacturing costs of solar cells. However, all previous attempts to integrate black silicon into solar cells have resulted in cell efficiencies well below 20% due to the increased charge carrier recombination at the nanostructured surface. Here, we show that a conformal alumina film can solve the issue of surface recombination in black silicon solar cells by providing excellent chemical and electrical passivation. We demonstrate that efficiencies above 22% can be reached, even in thick interdigitated back-contacted cells, where carrier transport is very sensitive to front surface passivation. This means that the surface recombination issue has truly been solved and black silicon solar cells have real potential for industrial production. Furthermore, we show that the use of black silicon can result in a 3% increase in daily energy production when compared with a reference cell with the same efficiency, due to its better angular acceptance.