The development of human dentition from adolescence to adulthood has been extensively studied by numerous dentists, orthodontists, and other experts in the past. While the prevention and cure of dental diseases and surgical reconstitution to address teeth anomalies, as well as research studies on teeth and the development of the dental arch during the growing-up years, have been the main concerns across the past decades, substantial effort has been made in recent years in the field of mathematical analysis of the dental arch curve, particularly in children from varied age groups and diverse ethnic and national origins. The proper care and development of primary dentition into permanent dentition are of major importance, and the dental arch curvature, whose study has been related intimately by a growing number of dentists and orthodontists to the prospective achievement of ideal occlusion and normal permanent dentition, has eluded a proper definition of form and shape. Many eminent authors have put forth mathematical models to describe the teeth arch curve in humans. Some have imagined it as a parabola, ellipse, or conic, while others have viewed it as a cubic spline. Still, others have viewed the beta function as the best way to describe the actual shape of the dental arch curve. Both finite mathematical functions and polynomials ranging from 2nd order to 6th order have been cited as appropriate definitions of the arch in various studies by eminent authors. Each such model has advantages and disadvantages, but none can exactly define the shape of the human dental arch curvature and factor in its features like shape, spacing, and symmetry/asymmetry. Recent advances in imaging techniques and computer-aided simulation have added to the attempts to determine dental arch form in children in normal occlusion. This paper presents key mathematical models and compares them through some secondary research study.