This paper presents an integrated, systems level view of several novel design and control features associated with the biologically-inspired, hexapedal, RiSE robot. RiSE is the first legged machine capable of locomotion on both the ground and a variety of vertical building surfaces including brick, stucco, and crushed stone at speeds up to 4 cm/s, quietly and without the use of suction, magnets, or adhesives. It achieves these capabilities through a combination of bio-inspired and traditional design methods. This paper describes the design process and specifically addresses body morphology, hierarchical compliance in the legs and feet, and sensing and control systems that enable robust and reliable climbing on difficult surfaces. Experimental results illustrate the effects of various behaviors on climbing performance and demonstrate the robot's ability to climb reliably for long distances.