Platinum chemotherapy remains the cornerstone of treatment for epithelial ovarian cancer (OC) and Poly (ADP-ribose) polymerase inhibitors (PARPi) now have an established role as maintenance therapy. The mechanisms of action of these agents is, in many ways, complementary, and crucially reliant on the intracellular DNA Damage Repair (DDR) response. Here, we review mechanisms of primary and acquired resistance to treatment with platinum and PARPi, examining the interplay between both classes of agents. A key resistance mechanism appears to be the restoration of the Homologous Recombination (HR) repair pathway, through BRCA reversion mutations and epigenetic upregulation of BRCA1. Alterations in non-homologous end-joint (NHEJ) repair, replication fork protection, upregulation of cellular drug efflux pumps, reduction in PARP1 activity and alterations to the tumour microenvironment have also been described. These resistance mechanisms reveal molecular vulnerabilities, which may be targeted to re-sensitise OC to platinum or PARPi treatment. Promising therapeutic strategies include ATR inhibition, epigenetic re-sensitisation through DNMT inhibition, cell cycle checkpoint inhibition, combination with anti-angiogenic therapy, BET inhibition and G-quadruplex stabilisation. Translational studies to elucidate mechanisms of treatment resistance should be incorporated into future clinical trials, as understanding these biologic mechanisms is crucial to developing new and effective therapeutic approaches in advanced OC.