Although the B0(s) and Lambda0(b) hadrons differ only in the spectator quarks from the well-studied B0(d) and b+(u) mesons, they provide a unique window on the physics of the b-quark. With no experiments presently running at the Z pole, hadron colliders now provide the best opportunity to study the B0(s) and the Lambda0(b). The collider experiments at the Tevatron, CDF and D0, have collected large numbers of B0(s) and Lambda0(b). Some of their latest preliminary measurements are presented here, including masses, lifetimes, and charmless decays. Progress is made toward measuring the lifetime difference Delta Gamma_s between the B0(s) mass eigenstates and the oscillation frequency Delta m_s.