Papillary lesions comprise a wide spectrum of lesions in terms of their clinical presentation, morphologic appearance, malignant potential, and clinical behavior. Their defining feature is that of a fibrovascular stromal core lined by epithelial and myoepithelial cells, attached to the wall of the duct and extending into the duct lumen. Papillary lesions are often diagnostically challenging both on core biopsy and in excision specimens. Much of the difficulty arises from the many different terminologies that are used to describe the various entities that are included under the umbrella term of papillary lesions. Separation of papillary lesions into categories with a meaningful clinical outcome is most appropriate; however, there is a relative paucity of well-designed outcome studies with substantial cohort numbers to provide information in this regard. We use a pragmatic approach to the classification of papillary lesions in our practice, as we will outline in this review. We will also discuss controversies surrounding papillary lesions and focus on management of these lesions on core biopsy and in excision specimens.