Thyroid carcinomas of follicular epithelial derivation are common and generally well-behaved malignancies with excellent cure and survival rates. However, a subset of these carcinomas, whether well-differentiated, poorly differentiated, or anaplastic, is highly aggressive, manifesting with local invasion, recurrence, and distant metastasis. The recognition of dedifferentiation is of paramount importance. In addition, the challenge for Pathologists is to identify the rare aggressive differentiated carcinomas so that treatment may be tailored appropriately. Thus, histological subtyping and documentation of other aggressive features such as widespread invasion and angioinvasion are critical. Mutational analyses in the past decade have delineated the molecular alterations responsible for thyroid carcinogenesis and progression, allowing greater sub-classification and prognostication of thyroid carcinomas. This review article highlights important aggressive morphologic features and molecular mutations associated with thyroid carcinoma.