The term “oncocyte” is derived from the Greek word “onkos,” meaning “swelling.” It is an epithelial cell defined by the presence of numerous mitochondria imparting a deeply eosinophilic finely granular appearance to the cytoplasm. In the thyroid gland, these cells have also been termed “Hurthle cells” or “Ashkanazy cells.” This chapter discusses the controversy of nomenclature of the cell of Hurthle cell lesions; is it oncocytic, oxyphilic, Hurthle, or Ashkanazy? It provides a historical review of nomenclature since its description in the nineteenth century, and describes the histology of these cells and their biological behavior and clinical significance. In addition, this chapter discusses oncocyte-like cells, which can also exhibit abundant eosinophilic cytoplasm, but differ from “true oncocytes.”