A climbing robot that can rapidly move on diverse surfaces such as floors, walls, and ceilings will have an enlarged operational workspace compared with other terrestrial robots. However, the climbing skill of robots in such environments has been limited to low speeds or simple locomotion tasks. Here, we present an untethered quadrupedal climbing robot called MARVEL (magnetically adhesive robot for versatile and expeditious locomotion), capable of agile and versatile climbing locomotion in ferromagnetic environments. MARVEL excels over prior climbing robots in terms of climbing speed and ability to execute various motions. It demonstrates the fastest vertical and inverted walking speed, whereas its versatile locomotion ability enables the highest number of gaits and locomotion tasks. The key innovations are an integrated foot design using electropermanent magnets and magnetorheological elastomers that provide large adhesion and traction forces, torque control actuators, and a model predictive control framework adapted for stable climbing. In experiments, the robot achieved locomotion on ceilings and vertical walls up to 0.5 meter (1.51 body lengths) per second and 0.7 meter (2.12 body lengths) per second, respectively. Furthermore, the robot exhibited complex behaviors such as stepping over 10-centimeter-wide gaps; overcoming 5-centimeter-high obstacles; and making transitions between floors, walls, and ceilings. We also show that MARVEL could climb on a curved surface of a storage tank covered with up to 0.3-millimeter-thick paint with rust and dust.