Dramatic progress has been made over the last decade in the numerical study
of quantum chromodynamics (QCD) through the use of improved formulations of QCD
on the lattice (improved actions), the development of new algorithms and the
rapid increase in computing power available to lattice gauge theorists. In this
article we describe simulations of full QCD using the improved staggered quark
formalism, ``asqtad'' fermions. These simulations were carried out with two
degenerate flavors of light quarks (up and down) and with one heavier flavor,
the strange quark. Several light quark masses, down to about 3 times the
physical light quark mass, and six lattice spacings have been used. These
enable controlled continuum and chiral extrapolations of many low energy QCD
observables. We review the improved staggered formalism, emphasizing both
advantages and drawbacks. In particular, we review the procedure for removing
unwanted staggered species in the continuum limit. We then describe the asqtad
lattice ensembles created by the MILC Collaboration. All MILC lattice ensembles
are publicly available, and they have been used extensively by a number of
lattice gauge theory groups. We review physics results obtained with them, and
discuss the impact of these results on phenomenology. Topics include the heavy
quark potential, spectrum of light hadrons, quark masses, decay constant of
light and heavy-light pseudoscalar mesons, semileptonic form factors, nucleon
structure, scattering lengths and more. We conclude with a brief look at highly
promising future prospects.Comment: 157 pages; prepared for Reviews of Modern Physics. v2: some rewriting
throughout; references update