Chronic infection of hepatitis C virus (HCV) leads to severe life-threatening liver diseases such as cirrhosis of liver, fibrosis and hepatocellular carcinoma (HCC). Severity of the disease infects >180 million people worldwide. In recent years, many computational approaches have been proposed to study and analyze the progression of liver fibrosis, HCC and other liver diseases developed from chronic HCV infection. In this article, we review the literature published in this area of study. Here we categorize all the approaches into two basic groups: analyzing gene expression and studying protein-protein interaction network among HCV-infected human proteins. We also review functional and pathway-enrichment analysis of HCV-interacted human proteins, which gives a clear understanding of functional perturbations leading to hepatocarcinogenesis. Topological analysis of HCV-human protein interaction network and HCV-HCC association network reveals important information of hepatocarcinogenesis progression in liver tissue. We compare the results of topological analysis performed in different studies. Moreover we observe that the HCV-interacted human proteins, which are also responsible for HCC progression, have relatively higher degree and betweenness centrality than that of the other HCV-interacted proteins.