This report details the developments in the field of perovskite/crystalline silicon (c-Si) tandem solar cells at EPFL-PVLAB since the SFOE-funded Synergy project, which ended in 2017. They were obtained in the frame of the PV2050 PNR70 project. A key milestone in the development of the technology was achieved in June 2018 with the demonstration of 2-terminal monolithic perovskite/Si tandem solar cells that feature a silicon heterojunction bottom cell textured on both sides for optimal light management. This novel cell design enabled to increase the cell efficiency from 22.7% for a configuration with a bottom cell mechanically polished on its front (status at the end of the Synergy project) to 25.2% for the fully textured cell architecture. This novel tandem design opens the path towards efficiencies >30% and is directly compatible with the Si heterojunction manufacturing process. But many challenges others than purely performance-related also need to be addressed before a commercial implementation of perovskite/c-Si tandems can be envisaged, notably with respect to longterm stability. This is the topic that this new SOFE-funded project aims to tackle: improving the stability of these state-of-the-art textured tandems, notably in reverse bias conditions, conditions that have so far led to an irreversible degradation of all the tested cells at EPFL PVLAB but also elsewhere.