Active galactic nuclei (AGN) display variability in their emission of radiation that can be used to probe the geometry and physical processes that drive them. In this thesis I examine the variability found in the emissions of X-ray, UV, and Optical radiation from AGN to constrain the properties of these extreme systems. To begin with I present optical interband time lags of the low-mass low±accretion rate AGN NGC 4395 using multiwaveband Liverpool Telescope and HiPERCAM Gran Telescopio Canarias data. The lags found here are consistent with X-ray reprocessing and suggest the first ever detection of the edge of the accretion disc in an AGN. I then present a study of X-ray/UV observations taken from XMM-Newton with simultaneous ground-based optical observations to measure the X-ray/UV/Optical lags of NGC 4395. These support the previous observations and gather further evidence for the existence of a truncated accretion disc in this object. Next I examine the long-term optical power spectrum of NGC 4395 using multiple light curves observed across different timescales. In addition I use simulation techniques to extend the previous X-ray observations and use reverberation modelling to create synthetic optical light curves from these. Comparison of the model fits of the data and the simulations suggest the existence of a secondary long-term source of variability in addition to X-ray reprocessing. Finally I investigate the X-ray to UV time lags of a different object, NGC 4593, using simultaneous XMM-Newton, Swift, and AstroSat observations. Here I find evidence of timescale-dependent lags. When filtered for short timescales the lags are consistent with X-ray reprocessing, but this suggests other long-term processes also exist within the object. I also note the presence of previously described contributions from the Broad Line Region's Balmer and Paschen continua.