Between 1992 to 1996, the CDF and D0 detectors each collected data
samples exceeding 100 pb^-1 of ppbar collisions at sqrt s = 1.8 TeV at the
Fermilab Tevatron.  These data sets led to a large number of precision
measurements of the properties of B hadrons including lifetimes, masses,
neutral B meson flavor oscillations, and relative branching fractions, and to
the discovery of the B_c meson.  Perhaps the most exciting result was the
first look at the CP violation parameter sin(2B) using the world's largest
sample of fully reconstructed B^0/B^0 -> J/psi K^0_s decays.  A summary of
this result is presented here.  In the year 2000, the Tevatron will recommence
ppbar collisions with an over order of magnitude expected increase in
integrated luminosity (1 fb^-1 per year).  The CDF and D0 detectors will have
undergone substantial upgrades, particularly in the tracking detectors and the
triggers.  With these enhancementsd, the Tevatron b physics program will
include precision measurements of sin(2B) and B^0_s flavor oscillations, as
well as studies of rare B decays that are sensitive to new physics.  The
studies of B^0_s mesons will be particularly interesting as this physics will
be unique to the Tevatron during the first half of the next decade.