Salivary gland-like and dermal analogue tumours of the breast are rare lesions that can be diagnostically challenging for pathologists. Data on the clinical behaviour and molecular characterisation of these mammary tumours are limited and their designation is mainly based on similar salivary gland or skin lesions. In this study, we present three cylindromatous breast tumours. These lesions were located within the breast, had ill-defined margins and were composed of nests containing a dual population of cytologically bland cells, surrounded at least partially by basement membrane-like material. The lack of cytological atypia and absence of mitoses led to the diagnosis of benign mammary cylindroma in 1 case. The expression of oestrogen receptor, focal absence of basement membrane material and the focal infiltrative nature together with patchy absence of peripheral basement membrane supported the diagnosis of malignancy in the other 2 cases. We discuss the morphological criteria, immunohistochemical profile and diagnostic pitfalls of these tumours. We also review the literature including previously reported cases of mammary cylindroma and differential diagnoses to be considered before making a diagnosis. We propose the term ‘mammary tumours with cylindromatous differentiation', implying their uncertain malignant nature, and propose management strategies.