The Neutrino Factory has been proposed as a facility to study neutrino oscillations to unprecedented accuracy, by means of an intense neutrino beam generated by decay of high energy muons. In a Neutrino Factory, muons undergo ionisation cooling to reduce the size of the muon beam and ultimately provide a more intense neutrino beam. In this seminar I describe a selection of the muon cooling devices that have been designed to provide longitudinal and transverse cooling. I also describe the effort to construct and operate the Muon Ionisation Cooling Experiment, a Proof-of-Principle cooling channel under construction at the Rutherford Appleton Laboratory. This may then pave the way for cooling and subsequent acceleration of extremely high density muon beams suitable for use as a Muon Collider.