The Muon Ionization Cooling Experiment (MICE) is under development at the Rutherford Appleton Laboratory (UK). The experiment's goal is to demonstrate ionization cooling, using a section of cooling channel. The final step of the experiment will be able to measure a 10% reduction in the emittance (transverse size) of a muon beam, with a relative precision of 1%. The emittance measurement will rely on inputs from scintillating fibre trackers, time-of-flight counters, transition Cherenkov detectors and the Electron-Muon Ranger, a fully active tracker-calorimeter at the downstream end. These detectors will together provide position, momentum and timing measurements of particles upstream and downstream of the experiment together with identification of particle species. The global reconstruction software, a part of the MICE Analysis User Software (MAUS), will combine the measurements from individual detectors into a set of complete particle hypotheses. Each 1 ms beam spill is reconstructed in parallel; a spill is divided into individual particle triggers and passed through a series of algorithms; track reconstruction and fitting, combined particle identification, and tagging and rejection of in-flight decays. The triggers are then recombined, and a collection of particle hypotheses are passed to the emittance analysis. We will discuss in detail the components of the global reconstruction, including: * Particle track matching through the quadrupole, solenoidal and time-varying RF fields of the beam optics. * Particle identification, using a combination of detector technologies and measurements. * The identification of in-flight particle decays, single hard multiple-scatters or multiple particles per trigger; each of which would invalidate MICE's 'single muon' analysis strategy.