Protoplanetary discs are flattened discs of gas and dust surrounding young stars that are believed to be the sites of planet formation. They are believed to be threaded by large-scale magnetic fields, which significantly affect their dynamics through processes such as the magneto-rotational instability (MRI), or the launching of a magnetic wind. Understanding the interplay between magnetic fields and protoplanetary disc structure and dynamics is crucial to shedding light on the origin of the complex features uncovered in recent observations of these systems, as well as the processes that contribute to planet formation. The paradigm that has emerged over the past two decades is that protoplanetary discs are weakly ionised, so that non-ideal magnetohydrodynamic (MHD) effects such as Ohmic resistivity, Hall drift, and ambipolar diffusion have a major impact on both the activity of the MRI and the geometry of the magnetic wind. They also affect the long-term radial transport of the large-scale magnetic field threading the disc, which in turn determines the magnetic flux distribution of the disc and has a feedback on the behaviour of the magnetic processes. To date, there is no self-consistent model that can at the same time capture both the impact of magnetic processes on disc structure and dynamics, and the evolution of the magnetic flux distribution. This work makes a contribution towards the realisation of such a model, by exploring the impact of non-ideal MHD effects on the disc’s magnetic flux transport, and how the interplay between magnetic processes under different conditions expected in protoplanetary discs influences the geometry of the magnetic field and disc dynamics.

The result from recent studies that protoplanetary discs are likely to be laminar in nature owing to the presence of non-ideal MHD makes it possible to simplify the problem to essentially one-dimensional vertical structure calculations based on radially local models. Although local models cannot capture the full properties of disc winds, they can nevertheless provide helpful insight into transport properties and geometry of the solutions that are found in global studies. To help gain understanding into the results and explore a large parameter space with potentially wide-ranging behaviour, I have invoked both semi-analytical techniques and numerical simulations in the investigation. I find that magnetic flux transport depends sensitively on both the inclination of the poloidal field and the non-ideal MHD effects that are present. In particular, the impact of Hall drift depends on whether the Hall parameter has the same sign as the scalar product between the magnetic field and disc rotation vector. The presence and profile of non-ideal MHD effects can lead to the excitation of large-scale MRI channel modes that contribute to the eventual geometry of the magnetic field in the disc and subsequent wind launching, while the specific long-term outcome can also depend on the initial conditions used. The results obtained in this Thesis are consistent with the flux transport rates and geometries obtained in previous studies of protoplanetary discs, and contribute to a deeper understanding of the underlying physics that are at play in disc-magnetic field interactions. This work paves the way to an eventual self-consistent theory of magnetised protoplanetary disc evolution and its consequences for planet formation.