This paper presents an autonomous planning and control framework for humanoid robots to climb general ladder- and stair-like structures. The approach consists of two major components: 1) a multi-limbed locomotion planner that takes as input a ladder model and automatically generates a whole-body climbing trajectory that satisfies contact, collision, and torque limit constraints; 2) a compliance controller which allows the robot to tolerate errors from sensing, calibration, and execution. Simulations demonstrate that the robot is capable of climbing a wide range of ladders and tolerating disturbances and errors. Physical experiments demonstrate the DRC-Hubo humanoid robot successfully mounting, climbing, and dismounting an industrial ladder similar to the one intended to be used in the DARPA Robotics Challenge Trials.