Preliminary results for Higgs boson production in $pp$ collisions at a centre-of-mass energy of 13 TeV performed by the ATLAS Collaboration in the decay channel $H \rightarrow ZZ^* \rightarrow \ell^+ \ell^− \ell'^+ \ell'^−$, where $\ell,\ell^{'}=e\text{ or }\mu$, are presented. These results are based on an integrated luminosity of 3.2 fb$^{-1}$ collected in 2015 by the ATLAS detector at the LHC. The fiducial cross section after the selection cuts is reported as well as the total cross section, compared to new and updated results obtained at centre-of-mass energies of 7 and 8 TeV, repectively. Dark matter production in association with a Higgs boson decaying to $H \rightarrow ZZ^* \rightarrow 4\ell$ is searched for in events with large missing transverse momentum. Moreover, a search for a heavy Higgs boson in the $H \rightarrow ZZ^* \rightarrow 4\ell$ channel is performed for the mass range 200 to 1000 GeV assuming a narrow intrinsic width.

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