Planetary systems are generally described as isolated systems, containing the host star and the orbiting planetary bodies. However, recent observational and theoretical work has demonstrated that the architectures of planetary systems can be completely transformed by environmental perturbations, such as passing stars, binary interactions, or Galactic tides. Architectures of planetary systems with ages up to several Gyr are observed to correlate with their stellar-dynamical environment. This discovery has existential implications: if the stellar environment destabilises and transforms planetary systems, this presents a new and fundamental axis for planetary system evolution and habitability. The key questions are now: precisely through what physical mechanism does the environment perturb planetary systems? How are the planetary systems impacted? And over what timescales does this transformation take place? Addressing these questions requires combining expertise in (1) the dynamical modelling of planetary system perturbations, (2) the characterisation of the degree of perturbation in both modelled and observed planetary systems, and (3) the detailed characterisation of the stellar-dynamical environment in which planetary systems are evolving. Our interdisciplinary International Team at ISSI Bern connects each of these areas. Only with the requested support from ISSI will we be able to understand how the stellar environment sets the properties of planetary systems. That way, we will build a unique framework for the interpretation of Gaia and PLATO systems, and aid the target selection of the next generation of major space missions in this area, such as Ariel.