Narrow Line Type-1 Seyfert active galaxies can exhibit a high degree of variability in the X-ray regime. This thesis examines that variability in the context of reverberation models, in which a flare in activity has an extended, energy dependent, response. A novel method is developed for estimating the response function in different energy bands. This method is then applied to three AGN: Ark 564, 1H 0707{495, and NGC 4051. The striking evidence for reverberation revealed in Ark 564 leads to a more thorough examination of that object, combining spectral and temporal approaches to develop a plausible physical model for its behaviour. The preferred model is one in which the reverberation is due to scattering from hot Comptonizing material approximately 1500 light-seconds from the central source. This conclusion is reinforced by a simulation of the angular dependence of reflection by Comptonizing gas.