The Energetic X‐ray Timing Survey Telescope (EXIST) mission concept is under study as the Black Hole Finder Probe (BHFP), one of the three Einstein Probe missions in the Beyond Einstein Program in the current NASA Strategic Plan. EXIST would conduct an all‐sky imaging hard X‐ray (∼10–600 keV) survey with unprecedented sensitivity: about 5 × 10−13cgs over any factor of 2 bandwidth, or comparable to that achieved at soft X‐rays in the ROSAT survey. The proposed angular resolution of 5arcmin, temporal resolution of 10microsec, energy resolution of 1–4 keV over the broad band, and duty cycle of 0.2–0.5 for continuous coverage of any source provide an unprecedented phase space for timing and spectral studies of black holes —from stellar to supermassive, as well as neutron stars and accreting white dwarfs. The large sky coverage allows intrinsically rare events to be studied. One particularly exciting example is the possible detection of tidal disruption of stars near quiescent AGN. Super flares from SGRs could be detected out to the Virgo cluster. The large duty cycle and all sky monitor nature of the mission will enable QPOs from luminous AGN and BH X‐ray binaries to be studied on timescales not possible before. I provide an overview of the mission concept and Reference Design, the X‐ray timing science prospects for EXIST, and how these might be further optimized in the current Study for EXIST as the BHFP so that EXIST might include many of the desirable features of a next‐generation timing mission. © 2004 American Institute of Physics