The nature of DM interactions is unknown. If the DM is not charged under SM forces, it can communicate with it through so-called portal interactions. Renormalizable portals have received lots of attention in the past. However, in some models non-renormalizable portals can appear naturally as the leading interaction with the SM. Inclusive production cross-sections through these portals can be computed in a model independent fashion. In this way it is possible to put general constraints on a large class of Dark Sectors. High intensity experiments such as beam dumps and neutrino experiments offer a great opportunity to test these models, through specific signatures such as displaced vertices.