The encapsulated and noninvasive follicular variant of papillary thyroid carcinoma has been recently reclassified as noninvasive follicular thyroid neoplasm with papillary-like nuclear features (NIFTP). These tumors demonstrate indolent behavior. This change in nomenclature will have great clinical impact by avoiding overtreatment of patients with NIFTP lesions who in the past were diagnosed with thyroid carcinoma and typically received completion thyroidectomy followed by radioactive iodine ablation. The pathologic diagnosis of NIFTP requires surgical removal of the thyroid lesion or the lobe harboring it, and thorough sampling of the complete interface between the tumor capsule and the thyroid parenchyma, to exclude foci of invasion. From a cytologic point of view, the unequivocal differential diagnosis between NIFTP and infiltrative follicular variant of papillary thyroid carcinoma in fine-needle aspiration is close to impossible based on cellular and architectural features. Therefore, use of adjunct molecular testing on fine-needle aspiration specimens may be essential for the preoperative diagnosis of low-risk tumors such as NIFTP for appropriate patient management. This review discusses and summarizes the existing known literature on molecular characteristics of NIFTP tumors, so far reported, including cases retrospectively classified or prospectively diagnosed as NIFTP. Brief reference is also made to new and promising approaches applicable to the diagnosis of this tumor.