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I will discuss mass and scale hierarchies from a general perspective and argue that the hints we have observed for new physics at very high energy scales may in fact be a smokescreen, with the new physics lying much closer to accessible energies. I will then discuss recent progress in model building, focussing on clockwork models, along with their associated linear dilaton continuum limit, including some comments on connections with string-motivated scenarios. The last part of the talk will focus on the LHC phenomenology of this class of models, including a new LHC search strategy to look for evidence of new physics in Fourier space.