This is a phase III, randomised, double-blind, placebo-controlled, multi-centre study to assess the efficacy of olaparib maintenance monotherapy in relapsed high grade epithelial ovarian cancer patients (including patients with primary peritoneal and / or fallopian tube cancer) who have responded following platinum based chemotherapy. The study population will be enrolled as two separate cohorts that will enrol simultaneously. The confirmatory cohort will consist of patients who carry a somatic BRCA mutation (documented mutation in BRCA1 or BRCA2 that is predicted to be deleterious or suspected deleterious) which are detected in tumour material but absent from germline blood testing ; the exploratory cohort will include patients with a mutation (documented mutation predicted to be deleterious or suspected deleterious) in non BRCA HRR-associated genes which are detected in tumour material regardless of their germline status.