Connecting planetary systems at different stages of stellar evolution helps us understand their formation, evolution, and fate, and provides us with exclusive and crucial insights about their dynamics and chemistry. Post-main-sequence white dwarf and giant branch stars host planetary systems which include a variety of observed objects and phenomena, such as planetary debris discs, disintegrating and embedded asteroids, exo-comets, and photospheric metal pollution. Here, I provide a brief observational review of our current knowledge of these systems. I also highlight the transformative advances expected in upcoming years with the current and next generation of ground-based and space-based initiatives. Looming orders-of-magnitude increases in available data must be accompanied by novel theories and simulations in order to understand the results from this interdisciplinary and expanding research field.