They have fleets with hundreds of thousands of vehicles and command multibillion-dollar streams of revenue.

But in the rapidly shifting transportation landscape, even the Goliaths of the rental car industry — some of the best-known brands in the world — worry about being left behind.

That may explain why some of the largest rental car companies have spent several years waging a quiet legislative war against start-ups led by a company called Turo that are trying to change the way people rent and own vehicles. Turo is a peer-to-peer car-sharing company — think Airbnb for cars.