Abstract : The international Muon Ionization Cooling Experiment (MICE), site d at Rutherford Appleton Laboratory in the UK, aims to build and test one ce ll of a a realistic ionization cooling channel lattice. This comprises three Absorber-Focus-Coil (AFC) modules and two RF-Coupling-Coil (RFCC) modules. Both are technically challenging. The Focus Coils are dual-coil superconducting solenoids, in close proximity, wound on a common mandrel. Each pair of coils is run in series, but can be configured with the coil polarities in the same (solenoid mode) or opposite (gradient mode). At the center of each FC there is a 20-L liquid-hydrogen ab sorber, operating at about 14 K, to serve as the energy loss medium for the ionization cooling process. The longitudinal beam momentum is restored in the RFCC modules, each of whic h houses four 201.25-MHz RF cavities whose irises are closed with 42-cm diam eter thin Be windows. To contain the muon beam, each RFCC module also has a 1.4-m diameter superconducting coupling solenoid surrounding the cavities. B oth types of magnet are cooled with multiple 2-stage cryo-coolers, each deli vering 1.5 W of cooling at 4 K. Designs for all components are complete and fabrication is under way. Descri ptions of the various components, design requirements, and construction status will be described.