The ATLAS collaboration has measured the production of heavy flavoured bottom and charm hadrons in proton--proton collisions at the Large Hadron Collider (LHC) at centre of mass energies of $\sqrt{s}=5.02,7,8$ and $13~\rm TeV$. These measurements serve as an important test of QCD calculations. Production measurements of $J/\psi, \psi(2S), X(3872)$ charmonium states, as well as $b$-hadron and $J/\psi$ pairs are presented.