We reviewed the published information on the thyroid hormone system and the mathematical modelling associated with it. The important thyroid hormones, viz. T3 and T4, regulatory in various metabolic activities, are released as an outcome of complex interactions occurring in the hypothalamus, pituitary and thyroid gland via the synthesis and release of Thyrotropin-releasing hormone, Thyroid-Stimulating Hormone, and thyroid hormones, respectively. Various mathematical models had been proposed in the past to explain the function and regulation of these hormones. The models that interacted pituitary-thyroid systems provide a better understanding of the sensitivity of the pituitary to the feedback effect of thyroid hormones in the context of thyroid hormone excess and deficiency A computational thyroid model may capture the known aspects of thyroid physiology. These models also explain the mental disorder called periodic relapsing catatonia. Certain models used Langmuir adsorption isotherm to understand endocrinological homeostasis. Thus, the study of these models will help better understand the physiology and functions of the endocrine system and hormones, particularly, those related to thyroid glands.