This thesis describes the search for Dark Matter at the LHC in the mono-jet plus missing transverse momentum final state, using the full dataset recorded in 2012 by the ATLAS Experiment.  It is the first time that the number of jets is not explicitly restricted to one or two, thus increasing the sensitivity to new signals.  Instead, a balance between the most energetic jet and the missing transverse momentum is required, thus selecting mono-jet-like final states.   Collider searches for Dark Matter have typically used signal models employing effective field theories (EFTs), even when comparing to results from direct and indirect detection experiments, where the difference in energy scale renders many such comparisons invalid.  The thesis features the first robust and comprehensive treatment of the validity of EFTs in collider searches, and provides a means by which the different classifications of Dark Matter experiments can be compared on a sound and fair basis.