The epic fight over who controls the future of the car industry is about to get a whole lot more interesting.

Tesla Inc., the pioneer and pacesetter, has dominated the early rounds of the new-energy age, capturing investors’ imaginations with a vision for what the next generation of vehicles looks like and seizing the nascent market for fully electric cars.

In the other corner are giants of scale: Volkswagen AG and Toyota Motor Corp. The world’s two biggest automakers — each which sold roughly 10 or 11 cars for every one Elon Musk did last year — realize the age of the battery-powered vehicle is here and are gaming out how to stay on top.