In this article we investigate the modeling and computational aspects of the product-of-exponentials (POE) formula for robot kinematics. While its connections with Lie groups and Lie algebras give the POE equations mathematical appeal, little is known regarding its usefulness for control and other applications. We show that the POE formula admits a simple global interpretation of an open kinematic chain and possesses several useful device-independent features absent in the Denavit-Hartenberg (DH) representations. Methods for efficiently computing the forward kinematics and Jacobian using these equations are presented. In particular, the computational requirements for evaluating the Jacobian from the POE formula are compared to those of the recursive methods surveyed in Orin and Schrader [5].