Searches for New Physics at the LHC

The considerable centre-of-mass energy and luminosity provided by the Large Hadron Collider will ensure a discovery reach for new particles which extends well into the multi-TeV region. ATLAS and CMS have carried out many studies of the implications of this capability for Beyond the Standard Model physics, focussing in particular on models incorporating supersymmetry and extra dimensions. In this paper we summarise some key results of these studies.