“Batteries Not Included.” These are the three words most dreaded by parents as they anxiously watch their child open a gift. But once this technical hurdle is surmounted, battery-powered toys are truly awesome, as remote-control, or RC, cars chase the family cat under the dining-room table, helicopters and airplanes dive bomb little brothers and sisters, and toy robots march down long hallways, incinerating everything in their terrible paths.

Some of the most prized early battery-powered toys are the tin robots produced in postwar Japan. Flashy Jim from the 1950s featured a remote-control unit that held the toy’s batteries, while the Radicon Robot from the same decade was actually the first wireless remote-control toy. More traditional was Nomura’s Robotank-Z from the 1960s, which rolled on wheels that were hidden by lithographed tank treads, lit up, made noise, and moved red arms that ended in a claw. Bandai’s Moon Explorer, also from the 1960s, walked on blocky legs, shined a red beam of light from a third eye in the middle of its forehead, and featured an analog clock in its chest.

Model cars, of course, were perfect vehicles for hidden power sources. In 1965, A.C. Gilbert, the maker of Erector sets, produced a battery-powered Aston Martin, just like the one driven by James Bond. About a decade later, in 1976, Mego made a Ford Gran Torino just like the one on “Starsky and Hutch.” The red muscle car, with its trademark white stripe running down the sides and across the back of the car’s top, had a siren, lights, and changed direction when it ran into things like table legs or a wall...