Among the thyroid neoplasias originating from follicular cells, we can include well-differentiated carcinomas, papillary (PTC) and follicular (FTC) thyroid carcinomas, and the undifferentiated anaplastic (ATC) carcinomas. Several mutations in oncogenes and tumor suppressor genes have already been observed in these malignancies; however, we are still far from the comprehension of their full regulation-altered landscape. Even if only 2% of the human genome has the ability to code for proteins, most of the noncoding genome is transcribed, constituting the heterogeneous class of noncoding RNAs (ncRNAs), whose alterations are associated with the development of several human diseases, including cancer. Hence, many scientific efforts are currently focused on the elucidation of their biological role. In this review, we analyze the scientific literature regarding the involvement of microRNAs (miRNAs), long noncoding RNAs (lncRNAs), and pseudogenes in FTC, PTC, and ATC. Recent findings emphasized the role of lncRNAs in all steps of cancer progression. In particular, lncRNAs may control progression steps by regulating the expression of genes and miRNAs involved in cell proliferation, apoptosis, epithelial–mesenchymal transition, and metastatization. In conclusion, the determination of the diagnosis, prognosis, and treatment of cancer based on the evaluation of the ncRNA network could allow the implementation of a more personalized approach to fighting thyroid tumors.