Major advances have been made in CRC treatment in recent years, especially in molecularly driven therapies and immunotherapy. Despite this, a large number of advanced colorectal cancer patients do not benefit from these treatments and their prognosis remains poor. The landscape of DNA damage response (DDR) alterations is emerging as a novel target for treatment in different cancer types. PARP inhibitors have been approved for the treatment of ovarian, breast, pancreatic, and prostate cancers carrying deleterious BRCA1/2 pathogenic variants or homologous recombination repair (HRR) deficiency (HRD). Recent research reported on the emerging role of HRD in CRC and showed that alterations in these genes, either germline or somatic, are carried by up to 15–20% of CRCs. However, the role of HRD is still widely unknown, and few data about their clinical impact are available, especially in CRC patients. In this review, we report preclinical and clinical data currently available on DDR inhibitors in CRC. We also emphasize the predictive role of DDR mutations in response to platinum-based chemotherapy and the potential clinical role of DDR inhibitors. More preclinical and clinical trials are required to better understand the impact of DDR alterations in CRC patients and the therapeutic opportunities with novel DDR inhibitors.