The Mahler measure of polynomials was introduced by Mahler in 1962 as a tool to study transcendental number theory. In this talk, we discuss the relationship between Mahler measure and Beilinson's regulator. As an application, we show that, under some conditions, the Mahler measure of a three-variable polynomial can be expressed in terms of special values of the L-function of elliptic curves and the Bloch?Wigner dilogarithm. In certain four-variable cases, the Mahler measure can be written as a Q-linear combination of special values of the L-function of K3 surfaces and the Riemann zeta function.