This thesis investigates an area of beyond the Standard Model (BSM) phenomenology associated with the presence of additional light, “weakly interacting slim particles” (WISPs). Particular attention is given to the hidden photon, the gauge boson associated with an additional U(1) gauge group that mixes kinetically with hypercharge. The theoretical foundation of the interactions studied lies in effective field theory, and the first part of the thesis investigates a so-far untested aspect of effective theories, namely effective non-locality in particle propagation. There are no observable effects of hidden photons if they are massless. We investigate the impact on experimental signatures in the case that the hidden photon gets its mass during compactification from a higher dimensional theory. WISPs make good dark matter candidates, and are especially compelling in light of the lack of observation of heavy WIMP (“weakly interacting massive particle”) dark matter. Nonetheless, it is shown that if WIMP dark matter is composed of a Dirac fermion that couples to the SM only through a pseudoscalar, indirect detection may be our only experimental window, and that it may already be appearing as a gamma ray excess at the Galactic Centre. There is considerable interest in dark matter searches at beam dump facilities, in particular for light dark matter coupled through a similarly light mediator particle. We investigate this set up in the context of the E613 beam dump experiment. Owing to the light mediator, the low-Q^2 kinematic region of deep inelastic scattering is especially important. We present a new treatment of dark particle scattering in this region via a light vector mediator (such as a hidden photon), and find that it enhances constraints.