Waymo is accelerating its rollout of robotaxis in the U.S., adding four new cities in Texas and Florida last month as self-driving technology begins to penetrate mainstream America.

Why it matters: Armed with $16 billion in fresh capital from parent Alphabet and others, Waymo is quickly extending its lead over other players like Tesla and Amazon-owned Zoox, which are still mostly in testing mode.

Catch up quick: Phoenix was the first market to access Waymo's driverless ride-hailing service in 2020.

• Rides were initially limited to about a 50-square mile zone in the East Valley, but service has since expanded to 315 square miles across much of Phoenix, Scottsdale, Tempe, Mesa and Chandler.

By the numbers: Now in 10 cities, Waymo has doubled the number of markets it serves in a matter of months.

• It's laying the groundwork for service in at least 20 cities, and is on track to provide more than one million driverless rides per week by the end of the year.
• It has about 3,000 robotaxis deployed nationwide, including 500 in the Valley.

What we're watching: Waymo's robotaxis are adapting quickly to new markets, but basic operational challenges — such as charging and maintenance — could constrain network growth.

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Misreading local politics could foil Waymo's ambitious growth plans.

The big picture: Arizona welcomed Waymo to test on its streets in 2017, three years before it allowed public riders to hail a robotaxi.

• Former Republican Gov. Doug Ducey signed an executive orders in 2015 requiring state agencies to "undertake any steps necessary" to support the testing and operation of autonomous vehicles in the state.
• Since Waymo's arrival, politicians across the aisle have touted Arizona's business-friendly atmosphere as a beacon for innovation.

Reality check: Not all of America is so enthusiastic.

State of play: Self-driving cars are permitted in about half the country.

• In some big cities including Washington, D.C. and New York, laws will have to change for robotaxis to operate without a human operator onboard.
• In other places, the law is silent on driverless cars, which means it's open to interpretation — and debate.
• More worrisome for Waymo, potentially: City leaders in some places, including Boston and Seattle, are proposing new ordinances that would prohibit autonomous vehicles.

The intrigue: Waymo replaced its global head of public policy last year to deal with the mounting headwinds.

• Justin Kintz previously led the policy team at Uber during its early growth period, when the ride-hailing network was unwelcome just about everywhere.

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A Waymo robotaxi incident outside of a California elementary school in January suggests an AI brain would react faster than a human, but it's not that simple.

The big picture: This incident fits into a much larger debate about whether autonomous vehicles can match — or exceed — the safety of human drivers.

• The answer to that question is crucial to winning the public's trust as robotaxis spread quickly across America.
• People fear self-driving cars, yet nearly 40,000 people are killed each year in traffic accidents involving human drivers.

Catch up quick: The National Highway Traffic Safety Administration is investigating after a Waymo robotaxi struck a child who ran across the street from behind a double-parked SUV.

• Police said first responders evaluated the student, with her parent present, and did not report any injuries.

The intrigue: Waymo claims its driverless vehicle behaved as expected, slamming the brakes as soon as it detected the child, slowing from 17 mph to under 6 mph before making contact.

• A "fully attentive human driver" in the same situation would have hit the child at approximately 14 mph, according to Waymo's computer modeling.

Reality check: Reacting quickly isn't the only way to avoid crashes, safety experts tell Axios. Context, judgment and driving experience matter, too.

• A careful, competent human driver would have avoided a panic stop in the first place by adjusting their driving behavior amid the chaos of school drop-off — or taking a different route altogether, said AV safety expert Philip Koopman, emeritus professor at Carnegie Mellon University.

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If you still haven't tried a Waymo — what's the hold up?

Zoom in: Here are some tips from Axios' Martin Vassolo who jumped on the self-driving wagon earlier this year:

✅ Do's:

• Tap the tablet: The in-car screen allows passengers to control music, climate and ride functions.
• Wear your seatbelt. It's the right call in every ride ... but the Waymo won't start moving until you do buckle up.
• Try out the back right seat. You get a good view of the steering wheel spinning to make turns (if that sight doesn't freak you out).

❌ Don'ts

• Don't sit in the driver's seat. Feel free to sit shotgun, however.
• Don't touch the steering wheel or other driving controls. "Somebody from rider support will get on and say, 'Please don't do that,'" Waymo's Ethan Teicher told Axios.
• Don't smoke or vape in the car. You wouldn't do that with a human behind the wheel, would you?
• Don't expect the vehicle to speed. The vehicle follows the rules of the road and does not mimic other drivers' behaviors.