During every S phase, cells need to duplicate their genomes so that both daughter cells inherit complete copies of genetic information. Given the large size of mammalian genomes and the required precision of DNA replication, genome duplication requires highly fine-tuned corrective and quality control processes. A major threat to the accuracy and efficiency of DNA synthesis is the presence of DNA lesions, caused by both endogenous and exogenous damaging agents. Replicative DNA polymerases, which carry out the bulk of DNA synthesis, evolved to do their job extremely precisely and efficiently. However, they are unable to use damaged DNA as a template and, consequently, are stopped at most DNA lesions. Failure to restart such stalled replication forks can result in major chromosomal aberrations and lead to cell dysfunction or death. Therefore, a well-coordinated response to replication perturbation is essential for cell survival and fitness. Here we review how this response involves activating checkpoint signaling and the use of specialized pathways promoting replication restart. Checkpoint signaling adjusts cell cycle progression to the emergency situation and thus gives cells more time to deal with the damage. Replication restart is mediated by two pathways. Homologous recombination uses homologous DNA sequence to repair or bypass the lesion and is therefore mainly error free. Error-prone translesion synthesis employs specialized, low fidelity polymerases to bypass the damage.