The wakefield in a plasma created by a pulse of laser light or charged beam can provide accelerating electric fields of 1,000 times greater than conventional accelerating structures. It has been proposed to use a high-energy proton beam as the initiator of the wakefield to accelerate a witness beam of electrons to the TeV scale. This general concept along with how this may lead to a TeV lepton collider of a few kilometres long are discussed. A collaboration of scientists have proposed to CERN a proof-of-principle experiment using protons from the SPS beam. The status of this proposal and prospects for the experiment are outlined.