Muon beams of low emittance provide the basis for intense, well characterised neutrino beams at Neutrino Factory and lepton-antilepton collisions up to several TeV at Muon Collider. The international Muon Ionization Cooling Experiment, MICE will demonstrate muon ionization cooling, the technique proposed to reduce the phase-space volume occupied by the muon beam at such facilities. To obtain sustainable ionization cooling, the muon beam loses transverse and longitudinal momentum via ionization energy loss in material (absorber) and then has the longitudinal momentum restored in an RF cavity. The combined effect is to reduce the transverse emittance of the beam. The design of the cooling demonstration experiment will be presented together with a summary of the performance of each of its components.