In this paper I consider the estimation of multi-factor exponential affine models of the term structure of interest rates. I start with a survey of the empirical work on the term structure in continuous time, showing that in most cases the implementation of the models has not fully exploited the theoretical restrictions. I also show that these works have almost always focused on "generalizations" of the theoretical model based on the inclusion of measurement errors in bills and bonds prices. I then suggest two approaches to statistical inference: the first is based on the Kalman filter, while the second follows the indirect inference approach. I also briefly discuss the relative properties of the two estimators, and I conclude with a small Monte Carlo experiment for a one-factor Cox-Ingersoll-Ross model, whose results are rather encouraging.