A rock-climbing robot is presented that can free climb on vertical, overhanging, and inverted rock faces. This type of system has applications to extreme terrain on Mars or for sustained mobility on microgravity bodies. The robot grips the rock using hierarchical arrays of microspines. Microspines are compliant mechanisms made of sharp hooks and flexible elements that allow the hooks to move independently and opportunistically grasp roughness on the surface of a rock. This paper presents many improvements to early microspine grippers, and the application of these new grippers to a four-limbed robotic system, LEMUR IIB. Each gripper has over 250 microspines distributed in 16 carriages. Carriages also move independently with compliance to conform to larger, cm-scale roughness. Single gripper pull testing on a variety of rock types is presented, and on rough rocks, a single gripper can support the entire mass of the robot (10 kg) in any orientation. Several sensor combinations for the grippers were evaluated using a smaller test-gripper. Rock-climbing mobility experiments are also described for three characteristic gravitational orientations. Finally, a sample acquisition tool that uses one of the robot's grippers to enable rotary percussive drilling is shown.