Oxidative- and endoplasmic reticulum (ER)-stress are common events during hepatitis C virus (HCV) infection and both regulate cell survival and determine clinical outcome. In response to intrinsic and extrinsic cellular stress, different adaptive mechanisms have evolved in hepatocytes to restore cellular homeostasis like the anti-oxidant response, the unfolded protein response (UPR) and the integrated stress response (ISR). In this review, we focus on the cellular stress response in the context of acute and chronic HCV infection. The mechanisms of induction and modulation of oxidative- and ER-stress are reviewed and analyzed from both perspectives: viral persistence and cell survival. Besides, we delve into the activation of the eIF2α/ATF4 pathway and selective autophagy induction; pathways involved in the elimination of harmful viral proteins after oxidative stress induction. For this, the negative role of autophagy upon HCV infection or negative regulation of viral replication is analyzed. Finally, we hypothesize that the cellular stress response in hepatocytes plays a major role for HCV control thus acting as an important host-factor for virus clearance during the early stages of HCV infection.