The existing constitutive models of concrete are mainly based on the framework of the classic elastic -plastic models which are rigorous on mathematics, but not coordinated with the failure mechanism of concrete. Researchers of different countries proposed various kinds of damage constitutive models based on the irreversible thermodynamics theory to describe the damage behavior of concrete. This paper presents a review of different models for concrete,analyzes the characteristics of each representative model and studies the scope of their application. On the basis of the review of existing concrete damage models, some new methods can be provided for further research on damage constitutive models.