Around 20% of main-sequence stars are known to host debris discs composed of planetesimals and the dust produced in their collisions. The structures of these discs can be constrained through spectral energy distribution (SED) modelling or direct imaging of the dust. Gravitational perturbations in a system containing planets or multiple stars can influence the evolution of a disc and leave observable signatures in the disc’s structure, potentially allowing the inference of companions which are not directly detectable. Additionally, one might expect the properties of discs to be related to the properties of massive companions at the population level, either because companions are linked to planetesimals through common formation conditions, or because of their gravitational influence following their formation.

In this thesis, I explore several issues relating to the connection between debris discs and massive companions. Motivated by the discovery of several discs with gaps, I begin by investigating one mechanism which may produce such gaps: eccentricity excitation through secular resonance with a two-planet system. I use Laplace-Lagrange theory to illustrate how the properties of undetected planets in a system with a gapped disc may be constrained within the secular resonance model, then use N-body simulations with collisional post-processing to show that the model can produce a gap at a specified location, but with inevitable asymmetries. Next, I study a sample of 341 multiple star systems, using their SEDs to identify and characterise their debris discs. I find that the stellar separation distributions of disc-bearing and disc-free systems differ with 99.4% confidence. No discs are detected for separations between 25 and 135 au, likely because such systems dynamically clear out circumstellar material at an early stage. Finally, I compare the disc properties of 201 stars with known planets and 294 without. I find no evidence for a statistical difference in the disc fractional luminosity or temperature distributions of the two samples, once differences in binarity, spectral type and dust sensitivity are accounted for.