This dissertation explores the question of whether broad iron lines from the accretion disk can be used as viable diagnostic tools for constraining black hole spin. We begin by giving an overview of the importance of black hole angular momentum as a signature of General Relativity and as a means of testing this theory in the strong-field limit. We discuss the anatomy of the typical black hole/accretion disk system, focusing on the complex environments of active galactic nuclei, and in particular Seyfert-1 systems which we pursue in this work. After developing a robust technique for fitting the continuum and absorption parameters through a rigorous analysis of the XMM-Newton spectrum of the Sy-1 galaxy NGC 4593, we then discuss a new model we have developed that fits broad emission lines from the inner accretion disk. This model, kerrdisk, is fully relativistic and allows the black hole spin to be a free parameter in the fit. Using this model, we carefully analyze the 350 ks XMM-Newton spectrum of the Sy-1 source MCG--6-30-15, which has the broadest and best-studied iron line observed to date. Fitting for the black hole spin in this source, we conclude that a > 0.987 to 90% confidence. We then extend our source list to analyze the XMM-Newton spectra of nine other radio-quiet Sy-1 AGN that have previously been observed to harbor broad iron lines. We find that, given enough photons and a broad line indicative of an origin in the inner disk where relativistic effects are important, our new model enables us to place robust constraints on black hole spin. Four of our sampled AGN meet the criteria necessary to constrain spin. Those constraints are given, along with the full spectral fit to each source. Interestingly, the spins of these sources range from moderate (a ~ 0.5−0.7) to very high (a > 0.95), and we do not find any AGN consistent with non-rotating black holes. For those objects that had marginal spin constraints or none at all, we discuss the spectral fits and the probable reasons for the lack of robustness of our results. This is the first ever survey of black hole spin in type-1 AGN.