Accretion discs are staples of astrophysics. Tapping into the gravitational potential energy of the accreting material, these discs are highly efficient machines that produce copious radiation and extreme outflows. While interesting in their own right, accretion discs also act as tools to study black holes and directly influence the properties of the Universe.
Among many of the curious behaviors exhibited by black hole X-ray binaries are state transitions --- complicated cycles of dramatic brightening and dimming. Using X-ray observations, we show that the evolution of the accretion disc spectrum during black hole state transitions can be described by a variable disc atmospheric structure without invoking a radially truncated disc geometry. The accretion disc spectrum is also a powerful diagnostic for measuring black hole spin if the effects of the disc atmosphere are well-understood. Using statistical methods, we show that modest uncertainties regarding the disc atmosphere can lead to erroneous spin measurements.
Magnetic fields are fundamental to the accretion process, with recent observations providing suggestive evidence for strong disc magnetization. Performing numerical simulations of accretion discs, we study how weak-to-strong disc magnetization regimes influence dynamo activity and the properties of MRI-driven turbulence. We also demonstrate that a background poloidal magnetic flux is required to form and sustain a strongly magnetized accretion disc. This thesis motivates the need for understanding how magnetic fields affect the observed spectrum from black hole accretion discs.