Abstract:γ-TiAl alloys with low density and high stiffness are preferred structural materials for weight saving of aircraft engines. The present paper deeply reviews flow behavior and constitutive equations of γ-TiAl alloys compressed at elevated temperature. Deformation processing parameters, deformation history and adjusted preheating treatment, chemical compositions and initial microstructures are main factors that determine flow behavior of γ-TiAl alloys compressed at elevated temperature. The constitutive models describing flow stress-strain curves are segmented into genres, such as empirical models, model coupled with different softening mechanisms and models about deformation mechanisms. Arrhenius model and H-S model are deeply discussed. Also, constitutive model including softening mechanism and models involving deformation mechanisms are summarized and analyzed. It predicts that emphasis on further research in γ-TiAl alloys is to establish constitutive models involving multiphase coordinating deformation mechanisms.