Recent results from the ATLAS experiment at the LHC on the charmonium production
and on the $B_c$ production and decays are presented.
These include studies of the associated production of the $J/\psi$ meson and $W$ boson,
the measurement of $J/\psi$ and $\psi(\mathrm{2S})$ mesons differential production cross-sections,
the measurement of the differential ratios of the $B_c^+$ and $B^+$ production cross-sections,
and the new results on the $B_c^+$ decays to $J/\psi D_s^{(*)}$ final states.
The results are obtained with $pp$ collision data collected at centre-of-mass energies $\sqrt{s} = 8$ and 13 TeV.