A dividing cell has to duplicate its DNA precisely once during the cell cycle to preserve genome integrity avoiding the accumulation of genetic aberrations that promote diseases such as cancer. A large number of endogenous impacts can challenge DNA replication and cells harbor a battery of pathways to promote genome integrity during DNA replication. This includes suppressing new replication origin firing, stabilization of replicating forks, and the safe restart of forks to prevent any loss of genetic information. Here, we describe mechanisms by which oncogenes can interfere with DNA replication thereby causing DNA replication stress and genome instability. Further, we describe cellular and systemic responses to these insults with a focus on DNA replication restart pathways. Finally, we discuss the therapeutic potential of exploiting intrinsic replicative stress in cancer cells for targeted therapy.