We explore paleo-detectors as an approach to the direct detection of Weakly Interacting Massive Particle (WIMP) dark matter radically different from conventional detectors. Instead of instrumenting a (large) target mass in a laboratory in order to observe WIMP-induced nuclear recoils in real time, the approach is to examine ancient minerals for traces of WIMP-nucleus interactions recorded over timescales as large as 1 Gyr. Here, we discuss the paleo-detector proposal in detail, including background sources and possible target materials. In order to suppress backgrounds induced by radioactive contaminants such as uranium, we propose to use minerals found in marine evaporites or in ultra-basic rocks. We estimate the sensitivity of paleo-detectors to spin-independent and spin-dependent WIMP-nucleus interactions. The sensitivity to low-mass WIMPs with masses mχ 10 GeV extends to WIMP-nucleon cross sections many orders of magnitude smaller than current upper limits. For heavier WIMPs with masses mχ 30 GeV cross sections a factor of a few to ∼ 100 smaller than current upper limits can be probed by paleo-detectors.