A promising way to enhance the efficiency of CIGS solar cells is by combining them with perovskite solar cells in tandem devices. However, so far, such tandem devices had limited efficiency due to challenges in developing NIR-transparent perovskite top cells, which allow photons with energy below the perovskite band gap to be transmitted to the bottom cell. Here, a process for the fabrication of NIR-transparent perovskite solar cells is presented, which enables power conversion efficiencies up to 12.1% combined with an average sub-band gap transmission of 71% for photons with wavelength between 800 and 1000 nm. The combination of a NIR-transparent perovskite top cell with a CIGS bottom cell enabled a tandem device with 19.5% efficiency, which is the highest reported efficiency for a polycrystalline thin film tandem solar cell. Future developments of perovskite/CIGS tandem devices are discussed and prospects for devices with efficiency toward and above 27% are given.