High grade serous ovarian carcinoma (HGSOC) is the most common subtype of ovarian cancer and the major cause of gynaecological cancer-related deaths in the Western world. Overall survival for HGSOC patients has not improved over the last two decades, and the progressive evolution of chemotherapy resistance is common. The development of precision medicine approaches has been significantly impeded by the extreme genomic complexity underlying this disease. HGSOC is characterised by somatic copy number aberrations (CNAs) and structural variants driven by extreme chromosomal instability (CIN). Importantly, CIN is a key mediator of clonal diversity which fuels the development of treatment resistance. An increased understanding of underlying mechanisms and mutational processes causing CIN in HGSOC is therefore critical to predict outcomes and facilitate the identification of new therapeutic approaches. In this thesis, we aim to investigate the prevalence of centrosome abnormalities in HGSOC and their involvement in driving CIN. The centrosome is the main microtubule organising centre of a cell and plays a crucial role during cell division ensuring accurate chromosome segregation. Missegregation of chromosomes at high rates results in CIN; and supernumerary centrosomes have previously been associated with aneuploidy and poor disease outcome in several cancers. However, relatively little is currently known about centrosome abnormalities in HGSOC. Using > 300 clinical tissue samples and ∼70 ovarian cancer cell lines, we show that centrosome amplification (CA) is highly prevalent in HGSOC and displays marked tumour heterogeneity. We report that CA is associated with increased CIN and, importantly, genome subclonality. Consequently, we highlight CA and associated vulnerabilities/survival mechanisms as promising targets for novel treatment strategies in HGSOC. As part of this work, we also present novel and improved methods to study CNAs from cost-effective assays, such as shallow whole genome sequencing (sWGS), and show that copy number analyses on the absolute, and not the relative, scale are required to facilitate inter-sample and inter-patient comparisons and interpretations. In addition, we develop minimally-invasive circulating tumour DNA (ctDNA) monitoring in patient derived xenograft (PDX) mice using sWGS and copy number analyses. We illustrate the feasibility of this approach and show its sensitivity for modelling treatment response in pre-clinical studies. This provides an important opportunity to study copy number driven tumour evolution and drug resistance, and will improve pharmaceutical/pre-clinical studies testing advanced anti-cancer therapies. Overall, the work presented in this thesis contributes to an improved understanding of CNAs in HGSOC, and develops new approaches to define effective therapies for high CIN cancers.