Generally, rental vehicles are paid for by your auto insurance if you purchased optional “substitute transportation” coverage, and your vehicle is not drivable due to collision damage.  If you don’t have this coverage on your policy, it may be possible to get claim a rental through the other driver’s policy if the other driver is determined to be at fault for an accident.

Rental bills are usually paid up until the time your car is repaired or when you have been paid for the total loss of your vehicle.