Thyroid cancer, the most prevalent endocrine cancer, has gained significant global attention due to its impact on public health. Extensive research efforts have been dedicated to leveraging artificial intelligence (AI) methods for the early detection of this disease, aiming to reduce its morbidity rates. However, a comprehensive understanding of the structured organization of research applications in this particular field remains elusive. To address this knowledge gap, we conducted a systematic review and developed a comprehensive taxonomy of machine learning-based applications in thyroid cancer pathogenesis, diagnosis, and prognosis. Our primary objective was to facilitate the research community's ability to stay abreast of technological advancements and potentially lead the emerging trends in this field. This survey presents a coherent literature review framework for interpreting the advanced techniques used in thyroid cancer research. A total of 758 related studies were identified and scrutinized. To the best of our knowledge, this is the first review that provides an in-depth analysis of the various aspects of AI applications employed in the context of thyroid cancer. Furthermore, we highlight key challenges encountered in this domain and propose future research opportunities for those interested in studying the latest trends or exploring less-investigated aspects of thyroid cancer research. By presenting this comprehensive review and taxonomy, we contribute to the existing knowledge in the field, while providing valuable insights for researchers, clinicians, and stakeholders in advancing the understanding and management of this disease.