In recent decades the number of known planets has escalated from the eight solar system planets to over 5000 exoplanets; the focus has now shifted to their characterisation. Spectroscopic studies of white dwarfs ‘polluted’ by planetary material are a unique laboratory allowing measurements of their bulk composition. This thesis focuses on these polluted white dwarfs to observationally investigate how the material ultimately accretes onto the white dwarfs, and the inferences made about the composition of exoplanetary bodies.

These white dwarfs become polluted due to the scattering of exoplanetary bodies on star grazing orbits where they tidally disrupt, producing dusty debris detectable as excess infrared emission, and then subsequently accrete onto the white dwarf. The scattering and accretion are expected to be stochastic processes with variability predicted on human time-scales. Chapter 2 reports near-infrared (JHK) monitoring campaigns of the dust emission with the UKIRT/WFCAM and NTT/SOFI. Over timescales of hours, days, months, and years no statistically significant variation is found. Chapter 3 reports spectroscopic monitoring campaigns of the metal features in the white dwarfs using SALT/HRS and Magellan/MIKE. Across more than 10 years and thousands of sinking timescales, no unambiguous statistically significant variability in the amount of material in the photospheres of the white dwarfs is found. Both results agree that the processes driving the accretion do so at a constant rate.

Polluted white dwarfs with infrared emission tend to be the most heavily polluted systems. Chapter 4 presents the first composition studies from a novel programme which identifies new heavily polluted white dwarfs discovered from their infrared excess. The planetary material that polluted these seven white dwarfs are broadly consistent with rocky material, but show some compositional and geological diversity. Some of the white dwarfs appear to have accreted a fragment of a larger core-mantle differentiated body. Using oxygen budgeting, two white dwarfs are discovered to have accreted oxygen-rich material which may imply water-rich bodies. Also, evidence points towards one of the white dwarfs accreting material from two distinct planetary bodies, this challenges the commonly used assumption that there is one body in the white dwarf's atmosphere at once.