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Titanium and its alloys, owing to their properties like high strength, toughness, corrosion resistance and thermal stability, are employable in various engineering and medical applications. The properties of titanium alloys depend upon the processing routes and their final microstructure. Therefore, the present review paper compiles the deformation behaviour of various alloys during hot deformation using a physical simulation. Subsequently, the flow stresses are analysed and utilized to develop the processing maps and the constitutive equations that are advantageous for predicting deformation mechanisms during the hot deformation. Specific features reported in the flow stress curves include work hardening, flow softening and steady-state behaviour. In certain cases, the yield point drop and oscillatory behaviour or serrations are also observed. Softening and oscillatory behaviour is an indicator of either dynamic recrystallization or flow-instability, whereas yield discontinuity signifies locking and unlocking of dislocations. In the processing maps, high power dissipation efficiency, η, reveals safe processing conditions, and the η value higher than 40% demonstrates dynamic recrystallization or globularization in the deformed microstructure, whereas the instability domain expresses shear band, flow localization, void formation and wedge cracks in the deformed microstructure. Amongst all the constitutive equations, the Arrhenius-type hyperbolic sine equation is the most suitable for Ti alloys for calculating flow stress and predicting dominant deformation mechanism using activation energy Q and stress exponent n.