This thesis describes the application of state-of-the-art high-energy X-ray studies to the astronomical quest for understanding obscured active galactic nuclei (AGN). These AGN are supermassive black holes growing by accretion of matter located in the nuclei of galaxies. The material that feeds these black holes also obscures them from view, rendering them challenging to study. It is possible to study them by effectively 'X-raying' galactic nuclei to peer through these obscuring veils. Beginning with the proof-of-concept application of novel X-ray Monte Carlo codes to the Nuclear Spectroscopic Telescope ARray (NuSTAR) spectrum of a known heavily obscured AGN, the thesis establishes the relevant parameters that characterise the AGN spectrum and central black hole growth rate. Next the largest sample of known heavily obscured AGN is compiled, finding the strength of a prominent iron spectral feature to weaken with AGN power. This is puzzling, and suggests that there may be more hidden AGN than previously thought. Finally by combining an all-sky infrared selection with NuSTAR follow-up, new heavily obscured AGN are identified. Obscuration emits infrared radiation, meaning that the infrared-selected AGN catalogue should be representative of the underlying AGN population. The absence of such representative catalogues has continually plagued cosmological studies, and the resultant obscured AGN fraction will be strongly constraining for AGN models.

Though short-term X-ray variability has been studied for the active galaxy NGC 4945, long-term studies promise to contribute to our understanding of the processes involved in accretion onto supermassive black holes. In order to understand the relationship between black hole mass and breaks in the power spectral density (PSD), the long-term X-ray variability of NGC 4945 was studied over the energy range 8-30 keV. Observations occurred over the year 2006 using the Rossi X-ray Timing Explorer. The data was reduced using the package FTOOLS, most notably the scripts Rex and faxbary. Light curves were produced and a PSD was obtained using a Fast Fourier Transform algorithm. Preliminary studies of the light curve show greater X-ray variability at higher frequencies. This result complements previous studies of NGC 4945 by Martin Mueller. However, the PSD produced must go through further study before accurate results can be obtained. A way to account for the window function of the PSD must be found before the behavior at lower frequencies can be studied with accuracy and the relationship between black hole mass and the break in NGC 4945's PSD can be better understood. Further work includes exploration into ways to subtract the window function from the PSD, as well as a closer analysis of the PSD produced by averaging the data into logarithmic bins. The possibility of a better way to bin the data should be considered so that the window function would be minimized.

For light curves sampled on an uneven grid of observation times, the shape of the power density spectrum (PDS) includes severe distortion effects due to the window function, and simulations of light curves are indispensable to recover the true PDS. We present an improved method for comparing light curves generated from a PDS model to the measured data and apply it to a 50-day long RXTE observations of NGC 4945, a Seyfert 2 galaxy with well-determined mass from megamaser observations. The improvements over previously reported investigations include the adjustment of the PDS model normalization for each simulated light curve in order to directly investigate how well the chosen PDS shape describes the source data. We furthermore implement a robust goodness-of-fit measure that does not depend on the form of the variable used to describe the power in the periodogram. We conclude that a knee-type function (smoothly broken power law) describes the data better than a simple power law; the best-fit break frequency is {approx} 10{sup -6} Hz.