Fractional Calculus gives a generalisation of the common techniques of integration and differentiation. Although the origin of Fractional Calculus lies more than 150 years behind us, it is still quite unknown. Recently however, Phillips (1984,1985) used fractional calculus to derive the distributions of the Stein-Rule and SUB estimator and Knight (1986b) used it to find the moments of the 2SLS estimator. This paper gives an introduction to fractional calculus by showing the ideas behind the definitions, giving examples and some applications. At the end an attempt is made to show the relevance of this calculus for the different fields of Econometrics and to put it in a more general mathematical perspective.