This thesis presents a search for invisible decays of the Higgs boson using the vector boson fusion channel. This uses 36 fb--1 of proton-proton collision data at √s = 13 TeV using the ATLAS detector at the Large Hadron Collider. The experimental methods for understanding the signal and background processes as well as detector effects are described in detail. The search is carried out in several regions defined by kinematic requirements on the final-state objects, and the observed event yields are used in a profile-likelihood fit in order to constrain the backgrounds. The results are interpreted using a modified frequentist method and are found to be consistent with the Standard Model expectations. An upper limit of 34% (28% expected) at 95% C.L. is placed on the invisible branching ratio of the Higgs boson. Re-interpretation of these results in terms of dark matter is also discussed, in the context of the Higgs portal and other simplified models.