Before revision:  The aim of this article is to present both , theoretical foundations and empirical aspects . Starting from the first short rate models , namely the Vasicek and the Cox-Ingersoll-Ross ones, we then give  an overview of some properties of affine processes and explain their relation to affine term structure models.
After revision:  The aim of this article is to present both , theoretical foundations and empirical aspects . Starting from the first short rate models , namely the Vasicek and the Cox-Ingersoll-Ross ones, we then give an overview of the properties of regular affine processes and explain their relation to affine term structure models.