We demonstrate four-and two-terminal perovskite-perovskite tandem solar cells with ideally matched band gaps. We develop an infrared-absorbing 1.2-electron volt band-gap perovskite, FA(0.75)Cs(0.25)Sn(0.5)Pb(0.5)I(3), that can deliver 14.8% efficiency. By combining this material with a wider-band gap FA(0.83)Cs(0.17)Pb(I0.5Br0.5)(3) material, we achieve monolithic two-terminal tandem efficiencies of 17.0% with > 1.65-volt open-circuit voltage. We also make mechanically stacked four-terminal tandem cells and obtain 20.3% efficiency. Notably, we find that our infrared-absorbing perovskite cells exhibit excellent thermal and atmospheric stability, not previously achieved for Sn-based perovskites. This device architecture and materials set will enable "all-perovskite" thin-film solar cells to reach the highest efficiencies in the long term at the lowest costs.