No question about it: self-driving cars are big news. Already a long list of car models—from Honda, Volvo, GM, Ford, Audi, Mercedes, Tesla, and others—automate some aspects of driving. They offer smart cruise control that goes all the way down to 0 mph, meaning they can drive automatically in stop-and-go traffic, braking and accelerating without ever risking a collision. They can change lanes for you—or stay in the lane for you. They can self-parallel park or head-in park. About the only driving they can't yet do themselves is make turns.

The poster child for self-driving cars, of course, is Google's fleet. After driving themselves more than a million miles on public roads, these cars have caused only a single accident so far: a low-speed fender bender with a bus. (They've been in 17 more minor accidents, but all of those were caused by human-driven cars—for example, someone rear-ending the Google car at a stoplight.)

This is exciting stuff. Self-driving cars, in theory, could eliminate the crashes that kill 1.2 million people every year around the world. Trillions of dollars would never have to be spent on hospital stays and insurance payouts. The environment would benefit because driverless cars would take the most efficient route, never get lost and reduce congestion. But the real mindblower is what will come next: self-driving cars that you don't own. Robotic cars that you summon when you want a ride.

Some huge companies are making colossal investments to make this vision real. In February 2015 Uber raided Carnegie Mellon University's highly regarded robotics department, hiring away 40 of its top researchers.

This January, General Motors invested half a billion dollars in Uber's rival, Lyft, for the purpose of developing its own on-demand driverless cars—then topped that two months later by spending a reported $1 billion on Cruise Automation, an automotive tech company. Ford and Google plan a joint venture with similar goals.

Yes, self-driving cars are revolutionary. But on-demand driverless cars? The changes would be so massive and fast and global, there's almost nothing about daily transportation that wouldn't change—mostly for the better.

Inexpensive robotic rides would mean there would be no particular reason to own a car. You wouldn't have to buy one, maintain it, gas it up. You'd never be late because you had to push the snow off the windshield or shovel your driveway.

When you get into a robo-car, you won't have to wait for it to heat up in the winter (or cool down in summer). You'll never have to hunt for a parking space; the car will drop you at the entrance of your destination, then zoom away.

All the societal constructs designed to defend against lousy driving skills—speed limits, speeding tickets, guardrails, even car insurance—might become unnecessary.

Similarly, who will need driver's ed or a driver's license? Twelve-year-olds will get their own rides home from sleepovers. And it won't matter if you (or your parents) are too old, frail or disabled to drive; millions of homebound Americans will suddenly be liberated.

Drunk driving? No longer a problem; if you're not doing the driving, drink up! Feeling sleepy on your long drive? Your robo-Uber car can drive through the night as you nap. And teenagers? Text away!

Of course, there are plenty of details to be worked out [see “The Truth about ‘Self-Driving’ Cars,” by Steven E. Shladover]. Some are technical; most of today's driverless cars are still fooled by snow, for example, and don't understand a human officer directing traffic. Some are more remote, though still important: Will robo-taxis be safe from hackers? If they cause an accident, who's responsible—the owner, the carmaker or the software company?

If you prefer to drive yourself, you might still have that option. Some experts predict that self-driving cars in some form will become mainstream on public roads in about five years. It's time to start warming up to the new self-driving era; it's too late to change lanes now.