This paper describes a novel clamping technology called compliant electroadhesion, as well as the first application of this technology to wall climbing robots. As the name implies, electroadhesion is an electrically controllable adhesion technology. It involves inducing electrostatic charges on a wall substrate using a power supply connected to compliant pads situated on the moving robot. High clamping forces (0.2-1.4 Newton supported by 1 square centimeter of clamp area, depending on substrate) have been demonstrated on a wide variety of common building substrates, both rough and smooth as well as both electrically conductive and insulating. Unlike conventional adhesives or dry adhesives, the electroadhesion can be modulated or turned off for mobility or cleaning. The technology uses a very small amount of power (on the order of 20 microwatts/Newton weight held) and shows the ability to repeatably clamp to wall substrates that are heavily covered in dust or other debris. Using this technology, SRI International has demonstrated a variety of wall climbing robots including tracked and legged robots.