The Energetic X-ray Imaging Survey Telescope (EXIST) is a proposed very large area coded aperture telescope array, incorporting 8m2 of pixelated Cd-Zn-Te (CZT) detectors, to conduct a full-sky imaging and temporal hard x-ray survey each 95min orbit. With a sensitivity of ~0.05mCrab, it will extend the ROSAT soft x-ray and proposed ROSITA medium x-ray surveys into the hard x-ray band and enable identifiaiton and study of sources ~10-20X fainter than with the ~15-100keV survey planned for the upcoming Swift mission. At ~100-600keV, the ~1mCrab sensitivity is 300X that achieved in the only previous all-sky survey. EXIST will address a broad range of key science objectives: from obscured AGN and surveys for black holes on all scales, which constrain the acretion history of the universe, to the highest sensitivity and resolution studies of gamma-ray bursts it will conduct as the Next Generation Gamma-Ray Burst mission. We summarize the science objectives and mission drivers, and the results of a mission design study for implementation as a free flyer mission, with Delta IV launch. Key issues affecting the telescope and detector design are discussed, and a summary of some of the current design concepts being studied in support of EXIST is presented for the wide-field but high resolutoin coded aperture imaging and very large area array of imaging CZT detectors. Overall mission design is summarized, and technology development needs and a development program are outlined which would enable the launch of EXIST by the end of the decade, as recommended by the NAS/NRC Decadal Survey.