High-grade serous ovarian cancer (HGSOC), the most frequent and lethal form of ovarian cancer, exhibits homologous recombination deficiency (HRD) in 50% of cases. In addition to mutations in BRCA1 and BRCA2, which are the best known thus far, defects can also be caused by diverse alterations to homologous recombination-related genes or epigenetic patterns. HRD leads to genomic instability (genomic scars) and is associated with PARP inhibitor (PARPi) sensitivity. HRD is currently assessed through BRCA1/2 analysis, which produces a genomic instability score (GIS). However, despite substantial clinical achievements, FDA-approved companion diagnostics (CDx) based on GISs have important limitations. Indeed, despite the use of GIS in clinical practice, the relevance of such assays remains controversial. Although international guidelines include companion diagnostics as part of HGSOC frontline management, they also underscore the need for more powerful and alternative approaches for assessing patient eligibility to PARP inhibitors. In these companion reviews, we review and present evidence to date regarding HRD definitions, achievements and limitations in HGSOC. Part 1 is dedicated to technical considerations and proposed perspectives that could lead to a more comprehensive and dynamic assessment of HR, while Part 2 provides a more integrated approach for clinicians.