By comparison with ovarian carcinomas, borderline ovarian tumours are characterised clinically by superior overall survival, even in women with peritoneal spread. In this Review, we aimed to clarify the histological and clinical factors potentially defining a high-risk group in whom disease is likely to evolve to invasive disease. Invasive peritoneal implants (in serous borderline ovarian tumours) and residual disease after surgery were the two factors clearly identified. Other factors are controversial owing to increased risk of invasive recurrence: micropapillary patterns in serous borderline ovarian tumour, intraepithelial carcinoma in mucinous lesions, stromal microinvasion in serous lesions, and use of cystectomy in mucinous borderline ovarian tumours. The pathologist has a pivotal role in assessment of the borderline nature of ovarian tumours and in identification of high-risk criteria, most of which are histological. But, reproducibility of the histological interpretation of some of these potential criteria--eg, classification of peritoneal implants (particularly in desmoplastic subtype), stromal microinvasion, micropapillary patterns, and intraepithelial carcinoma in mucinous borderline ovarian tumours--remains unclear, and should be investigated.