  We report on the first fully differential calculation of the
next-to-next-to-leading-order (NNLO) QCD radiative corrections to the
production of bottom-quark pairs at hadron colliders. The calculation is
performed by using the $q_T$ subtraction formalism to handle and cancel
infrared singularities in real and virtual contributions. The computation is
implemented in the Matrix framework, thereby allowing us to efficiently compute
arbitrary infrared-safe observables in the four-flavour scheme. We present
selected predictions for bottom-quark production at the Tevatron and at the LHC
at different collider energies, and we perform some comparisons with available
experimental results. We find that the NNLO corrections are sizeable, typically
of the order of $25$-$35\%$, and they lead to a significant reduction of the
perturbative uncertainties. Therefore, their inclusion is crucial for an
accurate theoretical description of this process.
