Triple-negative breast cancers (TNBC), as a group of tumours, have a worse prognosis than stage-matched non-TNBC and lack the benefits of routinely available targeted therapy. However, TNBC is a heterogeneous group of neoplasms, which includes some special type carcinomas with a relatively indolent course. This review on behalf of the European Working Group for Breast Screening Pathology reviews the literature on the special histological types of BC that are reported to have a triple negative phenotype and indolent behaviour. These include adenoid cystic carcinoma of classical type, low-grade adenosquamous carcinoma, fibromatosis-like metaplastic carcinoma, low-grade mucoepidermoid carcinoma, secretory carcinoma, acinic cell carcinoma, and tall cell carcinoma with reversed polarity. The pathological and known molecular features as well as clinical data including treatment and prognosis of these special TNBC subtypes are summarised and it is concluded that many patients with these rare TNBC pure subtypes are unlikely to benefit from systemic chemotherapy. A consensus statement of the working group relating to the multidisciplinary approach and treatment of these rare tumour types concludes the review.