The human immunodeficiency virus (HIV) affects 34 to 46 million people worldwide. Of these, about 4 to 5 million people are coinfected with hepatitis C virus (HCV). Coinfection adds more severity to the two diseases. HIV accelerates the progression of HCV in dually infected patients. Having a count of CD4+ T cells below 200 cells/mm3 increases the risk of severe liver disease . Moreover, there is a higher risk of cirrhosis, end-stage liver disease, hepato-carcinoma, and hepatic-related death. On the other hand,  HCV infection appears to have a significant effect on the progression of HIV to AIDS defining illness and AIDS related mortality. 

Bearing the aforementioned ideas in mind, we review mathematical models for the coinfection of HIV and HCV. We will consider integer and non-integer order models. Important features of the models include treatment for both diseases, screening, unawareness and awareness of HIV infection, and condom use, coinfection in specific populations. Important inferences are drawn with respect to public health care measures.