This paper presents a measurement of the production cross-section of a $Z$ boson in association with $b$-jets, in proton-proton collisions at $\sqrt{s} = 13$ TeV with the ATLAS experiment at the Large Hadron Collider using data corresponding to an integrated luminosity of 35.6 fb$^{-1}$. Inclusive and differential cross-sections are measured for events containing a $Z$ boson decaying into electrons or muons and produced in association with at least one or at least two $b$-jets with transverse momentum $p_\textrm{T}>$ 20 GeV and rapidity $|y| < 2.5$. Predictions from several Monte Carlo generators based on leading-order (LO) or next-to-leading-order (NLO) matrix elements interfaced with a parton-shower simulation and testing different flavour schemes for the choice of initial-state partons are compared with measured cross-sections. The 5-flavour number scheme predictions at NLO accuracy agree better with data than 4-flavour number scheme ones. The 4-flavour number scheme predictions underestimate data in events with at least one b-jet.
Measurements of fiducial cross sections for the electroweak production of two jets in association with a Z-boson are presented. The measurements are performed using 20.3 inverse femtobarns of proton-proton collision data collected at a centre-of-mass energy of sqrt(s)=8 TeV by the ATLAS experiment at the Large Hadron Collider. The electroweak component is extracted by a fit to the dijet invariant mass distribution in a fiducial region chosen to enhance the electroweak contribution over the dominant background in which the jets are produced via the strong interaction. The electroweak cross sections measured in two fiducial regions are in good agreement with the Standard Model expectations and the background-only hypothesis is rejected with significance above the 5 sigma level. The electroweak process includes the vector boson fusion production of a Z-boson and the data are used to place limits on anomalous triple gauge boson couplings. In addition, measurements of cross sections and differential distributions for inclusive Z-boson-plus-dijet production are performed in five fiducial regions, each with different sensitivity to the electroweak contribution. The results are corrected for detector effects and compared to predictions from the SHERPA and POWHEG event generators.