We investigate the nuclear and global structure of elliptical galaxies, and the apparent disparity between the Nuker and Sérsic light-profile models. We show that the so-called ``power-law" galaxies in fact have Sérsic r1/n profiles over their entire observed radial range. Consequently, only three (Sérsic-profile) parameters are required to simultaneously describe both the inner (HST-resolved) and outer profiles of low-luminosity (M > -20.5 B-mag) elliptical galaxies. We also find that ``core galaxies" have Sérsic profiles with a (partially evacuated) single power-law core. We have developed a modified (5-parameter) Sérsic profile with a power-law core to model the complete radial extent of luminous galaxies with cores. In addition to quantifying the global stellar distribution in these systems, we have derived new estimates of their core radii and other central properties. Comparison of the central stellar deficits with the galaxies' black hole masses suggests that the number of (dissipationless) major mergers that have produced luminous elliptical galaxies is around 1-2, rather than 8-10, which agrees with theory and implies that the galactic merger history of the Universe is roughly an order of magnitude less violent than previous observational analyses had suggested. Support for proposal number HST-AR-09927.01-A was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.