  This Thesis describes the basic framework and applications of a relativistic
ray-tracing code for analyzing accretion processes around Kerr black holes. We
begin in Chapter 1 with a brief historical summary of the major advances in
black hole astrophysics over the past few decades. In Chapter 2 we present a
detailed description of the ray-tracing code, which is used to calculate the
transfer function between the accretion disk and the detector. In Chapter 3, we
employ a simple ``hot spot'' model to explain the frequencies and amplitudes of
quasi-periodic oscillations (QPOs). In Chapter 4, we introduce additional
features to the hot spot model to explain the broadening of the QPO peaks as
well as the damping of higher-frequency harmonics in the power spectrum. In
Chapter 5 we present a description of the structure of a relativistic
alpha-disk around a Kerr black hole, and the observed spectrum from such a
disk. The features of this modified thermal spectrum may be used to infer the
physical properties of the accretion disk and the central black hole. In
Chapter 6 we develop a Monte Carlo code to calculate the detailed propagation
of photons from a hot spot emitter scattering through a corona surrounding the
black hole. The coronal scattering has two major observable effects: the
inverse-Compton process alters the photon spectrum by adding a high energy
power-law tail, and the random scattering of each photon effectively damps out
the highest frequency modulations in the X-ray light curve.
