This thesis discusses methods to construct a term structure of interest rates up to maturities of 50 years and gives new insights about the dynamics of the long end of the yield curve. The thesis focuses on the Vasicek model, in which the parameters are estimated by the Kalman filter. The theoretical frameworks of the Vasicek model as well as the Kalman filter are discussed, as well as the results of the two, three, four and five factor versions of the Vasicek model. It is concluded that the model works significantly better for every extra factor added, up to the fourth factor. Especially considering the very long end of maturities, the four factor model gives graphically significantly better results than the two and three factor models. The five factor model performs better on paper, however the Likelihood Ratio Test leaves room for doubt in proving that the five factor model is significantly better than the four factor model, since the cut off value is close to the value of the test. Overall, the four and five factor model fit the data well for the short term and the long term interest rates. However, in times of financial crises the model seems to perform worse.