The last decades have seen the development of a profusion of theoretical models of the term structure of interest rates. The aim of this survey is to provide a comprehensive review of these continuous time modeling techniques of the term structure applicable to value and hedge default-free bonds and other interest rate derivatives. The originality of the survey lies in the fact that it provides a unifying framework in which most continuous-time term structure models can be nested and thus related to each other. Thus, we not only present the most important continuous-time term structure models in the literature but also provide a mathematically rigorous and unifying setting in which these models can be compared in terms of their similarities, distinguished in terms of their idiosyncratic features and in which their main contributions and limitations can easily be highlighted.