Abstract: The Mahler measure of a monic polynomial in one variable with complex coefficients is the product of the absolute values of those roots of the polynomial which occur outside the unit disc. In case the polynomial has integer coefficients this quantity has arithmetic significance and appears in several seemingly unrelated problems. In this talk we give a brief survey of such applications of Mahler's measure to Diophantine problems. In particular we will discuss recent results on Lehmer's conjecture, on the distribution of values of Mahler's measure, and applications to estimates for the number of algebraic numbers of fixed degree and bounded height.