The presence of a non-baryonic Dark Matter component in the Universe is inferred from the observation of its gravitational interaction. If Dark Matter interacts weakly with the Standard Model particles it may be produced at the Large Hadron Collider (LHC), escaping detection and leaving large missing transverse momentum as its signature. New results from the Dark Matter search programme of the ATLAS experiment are presented, based on LHC proton-proton collision data collected at a center-of-mass energy of 13 TeV.