•Biliary tract cancers (BTCs) are poor-prognosis malignancies.•Precision medicine in BTC is currently focused on IDH/FGFR, benefiting a minority.•New strategies for improving outcomes in patients with BTC are required.•DDR-deficiency (pre-existent/induced) could be central to new treatment strategies. Biliary tract cancers (BTCs), including cholangiocarcinoma, gallbladder cancer and ampullary cancers, are poor-prognosis malignancies. Most patients are diagnosed with advanced disease, when treatment is limited to palliative chemotherapy. First line chemotherapy is usually administered in the form of cisplatin and gemcitabine. Benefit from second line chemotherapy is still to be confirmed. Even though new systemic treatment targets have been recognised, especially in patients with intrahepatic cholangiocarcinoma (e.g. IDH and FGFR), there is an urgent need for novel treatment strategies. Genomic profiling of BTC is progressively becoming a reality which allows a better understanding of their biology and potential new targets. This review provides an insight into DNA Damage Repair (DDR) mechanisms, prevalence of DDR-deficient tumours in BTC, and the potential role of DDR in cancer development. Some form of DDR deficiency is expected to be present in around 25% of patients with BTC, and this knowledge could be exploited to potentially increase response to currently-available treatment strategies (chemotherapy, radiotherapy or immunotherapy). For patients with DDR-proficient tumours, drug inhibition of DDR could be instituted.