  We argue that high-precision lattice QCD is now possible, for the first time,
because of a new improved staggered quark discretization. We compare a wide
variety of nonperturbative calculations in QCD with experiment, and find
agreement to within statistical and systematic errors of 3% or less. We also
present a new determination of alpha_msbar(Mz); we obtain 0.121(3). We discuss
the implications of this breakthrough for phenomenology and, in particular, for
heavy-quark physics.
