A classical result known since the nineteenth century asserts that if F(z) is a modular form of weight k and t(z) is a nonconstant modular function on a Fuchsian subgroup of SL(2,R) of the first kind, then F(z), zF(z),... z^kF(z), as (multi-valued) functions of t, are solutions of a (k+1)-st order linear ordinary differential equations with algebraic functions of t as coefficients. This result constitutes one of the main sources of applications of modular forms to other branches of mathematics. In this talk, we will give a quick overview of this classical result and explain some of its applications in number theory.