Hepatitis C virus (HCV) is one of the most widespread and dangerous human pathogens. In most cases, hepatitis C develops into chronic conditions, which often escape antiviral therapy and cause damage to various organs and systems. The conditions include liver fibrosis, steatosis, and hepatocellular carcinoma. These diseases are currently linked to oxidative stress and endoplasmic reticulum (ER) stress, which are induced by virus proteins. At the same time, HCV disturbs the systems that protect cells from these stresses, thus avoiding their effect on the virus life cycle. The review analyzes recent data on the function of the cell defense system in HCV-infected and uninfected cells. In addition, the structure of the HCV genome and the main functions of virus proteins are summarized in brief.