Integrating inorganic–organic perovskite top cells with crystalline silicon or CIGS bottom cells into monolithic tandem devices has recently attracted increased attention due to the high efficiency potential of these cell architectures. To further increase the tandem device performance to a level well above the best single junctions, optical and electrical optimizations as well as a detailed device understanding of this advanced tandem architecture need to be developed. Here we present our recent experimental and theoretical results on monolithic tandem combinations of perovskite with crystalline silicon and CIGS, as well as tandem relevant aspects of perovskite single junction solar cells.