We report on the progress of the program to study eclipsing binaries (EBs) in the Local Group galaxies. The primary goals of the program are to determine accurate distances and physical properties of the stars, and to probe the structure and evolution of the host galaxies. In particular, the distance to the Large Magellanic Cloud (LMC) is critically important because this nearby galaxy is used to calibrate most of the important cosmic distance indicators such as Cepheid and RR Lyr variables. Over the last several years, we have demonstrated that the distance of the LMC can be reliably measured using selected eclipsing binaries. The combined analyses of the UV/optical spectrophotometry, radial velocities, and light curves yield the stars’ physical properties (mass, radius, T eff, luminosity, metal abundance) and accurate (2–3%) distances. So far, the physical properties and distances of four LMC EBs have been completed and give a distance to the centroid of the LMC of 48.3 ± 1.6 kpc. Several additional EBs in the LMC and the Small Magellanic Cloud have been observed and are being analyzed. Also several LMC EBs have been observed with FUSE (92 – 119 nm) to further refine values of T eff and interstellar absorption. As an extension of these studies, 19–20th mag EBs in M31 are being observed photometrically and spectroscopically. The results of this extragalactic EB program are discussed along with plans to use EBs to study the host galaxy structure.