Metal-halide perovskites are promising solution-processable semiconductors for efficient solar cells and show unexpectedly high diffusion ranges of photogenerated charges. Here, we study charge extraction and recombination in metal-halide perovskite back-contact devices, which provide a powerful experimental platform to resolve electron- or hole-only transport phenomena. We prepare thin films of perovskite semiconductors over laterally-separated electron- and hole-selective materials of SnO¬2 and NiOx, respectively. Upon illumination, electrons (holes) generated over SnO¬2 (NiOx) rapidly transfer to the buried collection electrode, leaving holes (electrons) to diffuse laterally as majority carriers in the perovskite layer. Under these conditions, we find recombination is strongly suppressed. Resulting surface recombination velocities are below 2 cm s-1, an order of magnitude lower than in the presence of both carrier types, and approaching values of high-quality silicon. We find diffusion lengths of electrons and holes exceed 12 µm in our horizontal polycrystalline device, an order of magnitude higher than reported in vertically stacked architectures. We fabricate back-contact solar cells with short-circuit currents as high as 18.4 mA cm-2, reaching 70% external quantum efficiency.