The classical Dufresne identity identifies the distribution of the infinite time integral of a geometric Brownian motion as an inverse gamma law. I will discuss how this identity (and various extensions by Matsumoto and Yor) show up in applications. I will also present some recent results (joint with B. Rider) on the matrix extensions of Dufresne identity. Here the Brownian motion on the general linear group plays the role of the geometric Brownian motion and the Wishart distribution shows up in place of the gamma distribution.