The processing regime relevant to superplasticity in the Ti-6Al-4V alloy is identified. The effect is found to be potent in the range 850-900°C at strain rates between 0.001/s and 0.0001/s. Within this regime, mechanical behaviour is characterised by steady-state grain size and negligible cavity formation; electron backscatter diffraction studies confirm a random texture, leaving grain-boundary sliding as the overarching deformation mechanism. Outside of the superplastic regime, grain size refinement involving recrystallisation and the formation of voids and cavities cause macroscopic softening; low ductility results. Stress hardening is correlated to grain growth and accumulation of dislocations. The findings are used to construct a processing map, on which the dominant deformation mechanisms are identified. Physically-based constitutive equations are presented which are faithful to the observed deformation mechanisms. Internal state variables are used to represent the evolution of grain size, dislocation density and void fraction. Material constants are determined using genetic-algorithm optimisation techniques. Finally, the deformation behaviour of this material in an industrially relevant problem is simulated: the inflation of diffusion-bonded material for the manufacture of hollow, lightweight structures.