In this natural history protocol, the use of methods for follow-up of patients using radiopharmaceutical tracers such as (131)I, (123)I, (99)mTc-Sestamibi, (111)Inpentetreotide and 18-FDG PET administered according to standard clinical practice indications, and 68Gallium-DOTATATE (Octreotate)-administered per research protocol as indicated. All radionuclides will be administered according to standard clinical practice indications and published guidelines. The limitations and significance of serum thyroglobulin (Tg) measurement for diagnosing tumor recurrence will be assessed. The study will permit a continued evaluation of the risk/benefit ratio of already established methods of administering (131)I therapy including the impact of pre-treatment dosimetric calculations and administration of lithium (a well established, yet not widely used, adjuvant to (131)I treatment), especially in selected cases of thyroid cancer in which high-dose (greater than 150mCi) (131)I therapy is clinically indicated.