The thyroid gland, which is sensitive to electromagnetic radiation, plays a crucial role in the regulation of the hormonal levels of the human body. Biosensors, on the other hand, are essential to access information and derive metrics about the condition of the thyroid by means of of non-invasive techniques. This paper provides a systematic overview of the recent literature on bioelectromagnetic models and methods designed specifically for the study of the thyroid. The survey, which was conducted within the scope of the radiation transmitter-thyroid model-sensor system, is centered around the following three primary axes: the bands of the frequency spectrum taken into account, the design of the model, and the methodology and/or algorithm. Our review highlights the areas of specialization and underscores the limitations of each model, including its time, memory, and resource requirements, as well as its performance. In this manner, this specific work may offer guidance throughout the selection process of a bioelectromagnetic model of the thyroid, as well as a technique for its analysis based on the available resources and the specific parameters of the electromagnetic problem under consideration.