Adenoid cystic carcinoma (ACC) of the breast is a rare special subtype of breast cancer characterized by the presence of a dual cell population of luminal and basaloid cells arranged in specific growth patterns. Most breast cancers with triple-negative, basal-like breast features (i.e., tumors that are devoid of estrogen receptor, progesterone receptor, and human epidermal growth factor receptor 2 expression, and express basal cell markers) are generally high-grade tumors with an aggressive clinical course. Conversely, while ACCs also display a triple-negative, basal-like phenotype, they are usually low-grade and exhibit an indolent clinical behavior. Many discoveries regarding the molecular and genetic features of the ACC, including a specific chromosomal translocation t(6;9) that results in a MYB-NFIB fusion gene, have been made in recent years. This comprehensive review provides our experience with the ACC of the breast, as well as an overview of clinical, histopathological, and molecular genetic features.