The Tevatron collider at Fermilab provides a very rich environment for the study of b-hadrons. Both the D0 and CDF experiments have collected a sample of about 1 fb{sup -1}. they report results on three topics: b-hadron lifetimes, polarization amplitudes and the decay width difference in B{sub s}{sup 0} {yields} J/{psi}{phi}, and B{sub s}{sup 0} mixing.

The authors present recent results on b-hadron lifetimes and mixing obtained from the analysis of the data collected at the Tevatron Collider by the CDF and D0 Collaborations in the period 2002-2004. Many lifetime measurements have been updated since the Summer 2004 conferences, sometimes improving significantly the accuracy. Likewise the measurement of the B{sub d} oscillation frequency has been updated. New limits on the B{sub s} oscillation frequency have been determined using for the first time Run II data.

The Tevatron experiments, CDF and D0, have produced a wealth of new B-physics results since the start of Run II in 2001. We've observed new B-hadrons, seen new effects, and increased many-fold the precision with which we know the properties of b-quark systems. In these proceedings, we will discuss two of the most fruitful areas in the Tevatron B-physics program: lifetimes and mixing. We'll examine the experimental issues driving these analyses, present a summary of the latest results, and discuss prospects for the future.

This short review reports on recent results from CDF and D0 experiments at the Tevatron collider on B°{sub s} mixing and the lifetimes of B°{sub s} and [Lambda]{sub b}.

The authors review recent results of B{sup ++} masses, mass and lifetime of B{sub c}{sup +} meson, and lifetimes of B{sub s}{sup 0} and {Lambda}{sub b}{sup 0} hadrons from Tevatron Run II.

After a five year upgrade period, the Fermilab experiments CDF and D0 are taking high quality data in Run II of the Tevatron Collider. We report on the start-up of both detectors and present a selection of first B physics results from the Tevatron. We also compare different B hadron producers such as the [Upsilon](4S) with the hadron collider environment and discuss general features of B physics at a hadron collider.