Breast cancer is the most common cancer among women globally. Genomic instability (GI) refers to the increased tendency to accrue genomic alterations. It drives heterogeneity and is a hallmark of cancer. Genomic integrity is closely guarded by several mechanisms, including DNA damage checkpoints, the DNA repair machinery, and the mitotic checkpoint. Alterations in these surveillance mechanisms cause GI. In breast cancer, several pathways maintaining genomic integrity are distinctly altered, including some that have been successfully exploited for therapeutic targeting. In this review, we comprehensively discuss the recent advances on the mechanisms of GI in breast cancer, highlighting DNA repair defects and chromosome segregation errors during mitosis. We further review the clinical implications and therapeutic potential of targeting GI in the era of precision medicine.