The direct detection of dark matter through its elastic scattering off nucleons is among the most promising methods for establishing the particle identity of dark matter . The current bound on the spin-independent scattering cross section is \sigma ^ { \text { SI } } < 10 ~ { } \text { zb } for dark matter masses m _ { \chi } \sim 100 ~ { } \text { GeV } , with improved sensitivities expected soon . We examine the implications of this progress for neutralino dark matter . We work in a supersymmetric framework well-suited to dark matter studies that is simple and transparent , with models defined in terms of four weak-scale parameters . We first show that robust constraints on electric dipole moments motivate large sfermion masses \tilde { m } \agt 1 ~ { } \text { TeV } , effectively decoupling squarks and sleptons from neutralino dark matter phenomenology . In this case , we find characteristic cross sections in the narrow range 1 ~ { } \text { zb } \alt \sigma ^ { \text { SI } } \alt 40 ~ { } \text { zb } for m _ { \chi } \agt 70 ~ { } \text { GeV } . As sfermion masses are lowered to near their experimental limit \tilde { m } \sim 400 ~ { } \text { GeV } , the upper and lower limits of this range are extended , but only by factors of around two , and the lower limit is not significantly altered by relaxing many particle physics assumptions , varying the strange quark content of the nucleon , including the effects of galactic small-scale structure , or assuming other components of dark matter . Experiments are therefore rapidly entering the heart of dark matter-favored supersymmetry parameter space . If no signal is seen , supersymmetric models must contain some level of fine-tuning , and we identify and analyze several possibilities . Barring large cancellations , however , in a large and generic class of models , if thermal relic neutralinos are a significant component of dark matter , experiments will discover them as they probe down to the zeptobarn scale .