Traditionally, B physics has been the domain of e+ e- machines operating on the Upsilon (4S) resonance or the Z0 pole. But the UA 1 Collaboration has already shown that B physics is feasible at a hadron collider environment (see for example Ref. [1]). The first signal of fully reconstructed B mesons at a hadron collider has been published by the CDF Collaboration in 1992 [2]. CDF reconstructed a handful of B+ --> J/psi K+ events in a data sample of 2.6 pb-1 taken during the Tevatron Run 0 at the end of the 1980's. Since then experimental techniques improved significantly. Especially with the development of high precision silicon vertex detectors, the study of B hadrons is now an established part of the physics program at hadron colliders.