Genome instability is an enabling characteristic of cancer that facilitates the acquisition of oncogenic mutations that drive tumorigenesis. Underlying much of the instability in cancer is DNA replication stress, which causes both chromosome structural changes and single base‐pair mutations. Common fragile sites are some of the earliest and most frequently altered loci in tumors. Notably, the fragile locus, FRA3B, lies within the fragile histidine triad (FHIT) gene, and consequently deletions within FHIT are common in cancer. We review the evidence in support of FHIT as a DNA caretaker and discuss the mechanism by which FHIT promotes genome stability. FHIT increases thymidine kinase 1 (TK1) translation to balance the deoxyribonucleotide triphosphates (dNTPs) for efficient DNA replication. Consequently, FHIT‐loss causes replication stress, DNA breaks, aneuploidy, copy‐number changes (CNCs), small insertions and deletions, and point mutations. Moreover, FHIT‐loss‐induced replication stress and DNA breaks cooperate with APOBEC3B overexpression to catalyze DNA hypermutation in cancer, as APOBEC family enzymes prefer single‐stranded DNA (ssDNA) as substrates and ssDNA is enriched at sites of both replication stress and DNA breaks. Consistent with the frequent loss of FHIT across a broad spectrum of cancer types, FHIT‐deficiency is highly associated with the ubiquitous, clock‐like mutation signature 5 occurring in all cancer types thus far examined. The ongoing destabilization of the genome caused by FHIT loss underlies recurrent inactivation of tumor suppressors and activation of oncogenes. Considering that more than 50% of cancers are FHIT‐deficient, we propose that FRA3B/FHIT fragility shapes the mutational landscape of cancer genomes.