The azimuthal anisotropies of particle yields observed in relativistic heavy-ion collisions have been traditionally considered as a strong evidence of the formation of a deconfined quark-gluon plasma produced in these collisions. However multiple recent measurements from the LHC experiments in $pp$ and $p$+Pb systems show similar features as those observed in Pb+Pb collisions, indicating the possibility of the production of such a deconfined medium in smaller collision systems.
This report presents a comprehensive summary of ATLAS measurements in $pp$ collisions at 2.76, 5.02 and 13~TeV and in $p$+Pb collisions at 5.02 and 8.16 TeV. It includes measurements of two-particle hadron-hadron correlations in $\Delta\phi$ and $\Delta\eta$, with a template fitting procedure used to subtract the dijet contributions. Measurements of multi-particle cumulants $c_n\{2-8\}$ are also presented. The standard cumulant measurements confirm presence of collective phenomena in $p$+Pb collisions, but are biased by non-flow correlations and are not able to provide evidence for collectivity in $pp$ collisions. To address this, measurements from a new sub-event cumulant method that suppresses the contribution of non-flow effects are discussed. Also the first measurements of $\mathrm{v}_2$ coefficient in $Z$-tagged $pp$ events and with $D^{\star\pm}$ mesons in the final state in $p$+Pb collisions are presented.