Measurements of the associated production of a $\mathrm{Z}$ boson with at least one jet originating from a b quark in proton–proton collisions at $\sqrt{s} = 8,\text {TeV} $ are presented. Differential cross sections are measured with data collected by the CMS experiment corresponding to an integrated luminosity of 19.8 $,\text {fb}^{-1}$ . $\mathrm{Z}$ bosons are reconstructed through their decays to electrons and muons. Cross sections are measured as a function of observables characterizing the kinematics of the $\mathrm{b}$ jet and the $\mathrm{Z}$ boson. Ratios of differential cross sections for the associated production with at least one $\mathrm{b}$ jet to the associated production with any jet are also presented. The production of a $\mathrm{Z}$ boson with at least two $\mathrm{b}$ jets is investigated, and differential cross sections are measured for the dijet system. Results are compared to theoretical predictions, testing two different flavour schemes for the choice of initial-state partons.