DNA replication is a fundamental process of the cell that ensures accurate duplication of the genetic information and subsequent transfer to daughter cells. Various pertubations, originating from endogenous or exogenous sources, can interfere with proper progression and completion of the replication process, thus threatening genome integrity. Coordinated regulation of replication and the DNA damage response is therefore fundamental to counteract these challenges and ensure accurate synthesis of the genetic material under conditions of replication stress. In this review, we summarize the main sources of replication stress and the DNA damage signaling pathways that are activated in order to preserve genome integrity during DNA replication. We also discuss the association of replication stress and DNA damage in human disease and future perspectives in the field.