Papillary neoplasms of the breast are a heterogeneous group of epithelial tumors nearly entirely composed of papillae. Their classification rests on the characteristics of the epithelium and the presence and distribution of the myoepithelial cells along the papillae and around the tumor. Papillary neoplasms of the breast can be diagnostically challenging, especially if only core needle biopsy (CNB) material is available. This review summarizes salient morphological and immunohistochemical features, clinical presentation, and differential diagnoses of papillary neoplasms of the breast. We include a contemporary appraisal of the upgrade rate to carcinoma (invasive carcinoma and ductal carcinoma in situ [DCIS]) and atypical hyperplasias in surgical excision specimens obtained following CNB diagnosis of papilloma without atypia, and a review of the available follow-up data in cases without immediate surgical excision.