Status of the observed and predictedbb¯production at the Fermilab Tevatron

We review the experimental status of the $b$-quark production at the Fermilab Tevatron. We compare all available measurements to perturbative QCD predictions (NLO and FONLL) and also to the parton-level cross section evaluated with parton-shower Monte Carlo generators. We examine both the single $b$ cross section and the so called $b\overline{b}$ correlations. The review shows that the experimental situation is quite complicated because the measurements appear to be inconsistent among themselves. In this situation, there is no solid basis to either claim that perturbative QCD is challenged by these measurements or, in contrast, that long-standing discrepancies between data and theory have been resolved by incrementally improving the measurements and the theoretical prediction.