The explicit search for exotic decays of the 125 GeV Higgs boson presents a largely untapped discovery opportunity for the LHC collaborations, as such decays may be easily missed by other searches. A large set of new experimental analyses are possible on the existing and forthcoming data from the LHC. The Higgs is uniquely sensitive to the potential existence of new weakly coupled particles and there is a large class of both simplified and complete models that give rise to characteristic patterns of exotic Higgs decays. The status of exotic Higgs decays after LHC Run 1 will be assessed. In many cases new nontrivial constraints can be set by reinterpreting existing experimental analyses. Improvements are possible with dedicated analyses. These analyses can be prioritized according to their theoretical motivation and their experimental feasibility.