The classical uniformization theorem states that every Riemann surface carries a complete constant curvature Riemannian metric in its conformal class. It is difficult to algorithmically implement the uniformization theorem for polyhedral surfaces. We introduce a notion of discrete conformality for polyhedral surfaces and prove a discrete version of the uniformization theorem for compact polyhedral surfaces. This is a joint work with David Gu, Jian Sun and Tianqi Wu.