The study of warped discs and the study of magnetised discs have generally been performed in relative isolation, and comparatively little attention has been given to the complex interplay between these two aspects of accretion disc physics. This thesis aims to provide a synthesis of these disparate areas of research and explore the effects of a mean magnetic field on warp evolution.

Using a coordinate system based upon tilted spheres, a series of self-similar solutions are presented for the global structure of a potential magnetic field beyond a warped disc. Warped discs threaded by a mean magnetic field are investigated numerically and semi-analytically in both a warped shearing box and a corrugated disc model. An asymptotic analysis is used to demonstrate the relation between these distinct local perspectives. Interactions between the warp and what we have called ‘Alfv$\acute e$nic-epicyclic’ oscillation modes, the magnetic analogues to epicyclic oscillations, are found to have potentially profound and hitherto unexplored consequences for the evolution of the warp. Resonances between the vertical oscillation mode and the Alfv$\acute e$nic-epicyclic modes imbue magnetised discs with a rich and subtle structure compared to their hydrodynamic counterparts. Notably the anomalous rapid propagation of the warp in Keplerian inviscid discs is suppressed, while warp propagation in non-Keplerian discs may be considerably enhanced. Non-local angular momentum transport via the external magnetic field may also provide an additional important contribution to the warp evolution. The practical application of these results to numerical simulations is discussed.