Borderline ovarian tumors (BOT) are uncommon but not rare epithelial ovarian neoplasms, intermediate between benign and malignant categories. Since BOT were first identified >40 years ago, they have inspired controversies disproportionate to their incidence. This review discusses diagnostic criteria for the histologic subtypes of BOT, highlighting areas of diagnostic challenges, ongoing controversies, and changes in terminology implemented by the recent 2014 WHO Classification of Tumours of the Female Genital Organs. Emerging knowledge supports the notion that subtypes of borderline ovarian tumors comprise distinct biologic, pathogenetic, and molecular entities, precluding a single unifying concept for BOT. Serous borderline tumors (SBT) share molecular and genetic alterations with low-grade serous carcinomas and can present at higher stages with peritoneal implants and/or lymph node involvement, which validates their borderline malignant potential. All other (non-serous) subtypes of BOT commonly present at stage I confined to the ovary(ies) and are associated with overall survival approaching that of the general population. An important change in the WHO 2014 classification is the new terminology of non-invasive implants associated with SBT, as any invasive foci (previously called "invasive implants") are now in line with their biological behavior considered peritoneal low-grade serous carcinoma (LGSC). The controversy regarding the terminology of non-serous borderline tumors, called by some pathologists "atypical proliferative tumor" in view of their largely benign behavior, has not been resolved. The concepts of intraepithelial carcinoma and microinvasion may evolve in further studies, as their presence appears to have no prognostic impact and is subject to considerable inter-observer variability.