This paper proposes an underactuated modular climbing robot with flat dry elastomer adhesives. This robot is designed to achieve high speed, high payload, and dexterous motions that are typical drawbacks of previous climbing robots. Each module is designed as a tread-wheeled mechanism to simultaneously realize high speed and high adhesive force. Two modules are connected by compliant joints, which induce a positive preload on the front wheels resulting in stable climbing and high payload capacity. Compliant joints also help the robot to perform various transitions. An active tail is adopted to regulate the preload of the second module. Force transfer equations are derived and stable operating conditions are verified. The stiffness coefficients of the compliant joints and the active tail force are determined optimally to satisfy the constraints of stable operation. The prototype two-module robot achieves 6-cm/s speed and 500-g payload capacity on vertical surfaces. The abilities of flat surface locomotion, internal, external, and thin-wall transitions, and overcoming various sized obstacles are validated through experiment. The principle of joint compliance can be adopted in other climbing robots to enhance their stability and transition capability.