A basic yet comprehensive presentation of the genesis of subgrade modeling in foundation engineering and the subgrade models that have evolved from this over the past two centuries beginning with the 19th century work of Fuss and Winkler. This scholarly monograph reflects Dr. Horvath's 45 years of research into this topic and contains never-before-published material including worked examples using case history applications. This document debunks the long-held assumption that the coefficient of subgrade reaction, k, is an inherent soil properly and also unlocks the many mysteries and uncertainties of subgrade models by illustrating how all subgrade models, whether based on a simplified elastic continuum or an assemblage of mechanical elements, are approximate solutions to the same, unifying stress-displacement problem in the theory of elasticity. Also illustrated is how hybrid subgrade models offer the best of all worlds for routine use in practice. This document is intended to be of use to both structural and geotechnical design professionals in practice as well as academic instructors and researchers.