We examine a variety of X-ray and optical data for evidence of evolution in the accretion structure of the dipping, eclipsing, bursting low-mass X-ray binary (LMXB) EXO 0748-676. Our results are divided into three main sections. New ASCA and archival EXOSAT data reveal behavior related to the source brightness state. An anomalous dip (Φ ≅ 0.45) can be associated with the source low state. This dip does not appear to precess and is the only dipping feature showing significant changes between brightness states. The quiescent (non-dipping, non- bursting, non-eclipsing) spectral behavior evolves between high and low states. The hardness of quiescent spectrum is uncorrelated with intensity in the high state, but becomes anti-correlated with intensity in the low state. Origins of the anti-correlated behavior are not clear, but could be related to an absorption component not present in the high state. We proceed to examine the moderate X-ray resolution spectra of EXO 0748-676 in two different brightness states. Spectra were obtained from both BBXRT on 1990 December 6 (high state) and ASCA on 1993 May 7 (low state). The greatest difference between the spectra of the source in either state is that a previously un-noted soft (<2 keV) X-ray excess exists in the low state spectrum of this source. We show the new soft component exists in all intensity selected spectra. A line-like feature is seen to develop as the source goes into its dipping state. Lastly, Optical and X-ray observations of EXO 0748-676 in late March 1989 show the mean X-ray and optical flux levels during this period do not reflect similar system states. The optical counterpart is found to be in an intermediate to low state (VΦ=0.5 = 17.18 +/- 0.03) while X-ray data imply a high state. The changed relationship between optical/X-ray is evidence showing that EXO 0748-676 has evolved into a new emission `mode'. Lack of correlated variability in these simultaneous X-ray/optical data may be a result of strong modulation in the optical lightcurve originating from the accretion structure. We evaluate these results in terms of the current models of the accretion geometry of this system. Taken piecemeal, our observations of the dipping behavior can largely (but not entirely) be explained by either model. However, when we attempt to explain the changes in the dipping behavior as a whole, and when we consider our other results for the X-ray spectrum, X-ray colors and the optical/X-ray behavior these models fail. We find that we may resolve the difficulties of the current models in our new, ``Hybrid'' model of the accretion structure. Our Hybrid model is based on the work of Frank, King & Lasota (1987) but incorporates three fundamental changes: (1)the accretion structure that resides at Rcirc is shifted by 0.15 phase, (2)we relax the condition that the outer accretion disk and overflowing accretion stream cannot be irradiated and (3)we require that the dipping material located at Rcirc be irradiated less even as the system X-ray luminosity increases. We demonstrate that the Hybrid model can make up most of the deficiencies of the current models of the accretion structure in LMXB. We find difficulty in explaining only the long term shift in the reprocessing relationship of EXO 0748-676 using the Hybrid model.