Precision B-physics results from the CDF and D0 Collaborations
based on data collected during the Tevatron 1992-96 run are presented.  In
particular we discuss the measurement of the B_s meson lifetime, B_c meson
observation, and B^0-B-bar^0 mixing results obtained using time-evolution
analyses.  Prospects for the next Tevatron run, starting in 1999, are also
reported.