In this thesis I study single and binary stars and the evolution of planetary systems as the primary star evolves into a white dwarf. White dwarfs are the end point for 97% of stars in the Galaxy, but they are far from the end of its activity. White dwarfs can be sites of astrophysical activity via interactions with companion stars, planets and other small bodies. I first study the potential for planetary formation in evolving binaries due to mass transfer between stellar components. I estimate ~30 million second and ~3.5 million third generation planets in our Galaxy can form as a result of mass transfer and give parameters of the binary systems where this may occur. Following from this work I focused on a specific type of binary that may transfer mass in the future: a close white dwarf-brown dwarf (WD-BD) binary. These systems are highly uncommon and can act as proxies for large gaseous planets. I used observations of 24 WD-BDs candidates and found one that is potentially a true WD-BD binary. This binary assists research on survival through the common envelope phase, evolution of high mass ratio binaries and atmospheric irradiation. Finally I explored the fate of planets and other small bodies. Polluted white dwarfs are thought to be the remnants of tidally destroyed planetesimals that have accreted onto the WD surface. In the current literature the main mechanism for accretion cannot explain high accretion rates or the lack of observed discs. I used a magnetic field to decrease the lifetime of a disc of debris. I found that a field strength of 10 Kilo-Gauss is enough to shorten the lifetime of a disc and increase the accretion rate of the debris onto the surface. This method has not been used before this work and opens up a new area of research into polluted magnetic white dwarfs.