Once the initial surprise of the accident has settled, you will need to address repairs to the rental car and associated damage. Your personal auto insurance policy may cover the costs through two primary components:

Collision insurance coverage helps pay for damage to your vehicle if you are in an accident with another vehicle or an object once you pay your deductible. The deductible is what you pay out of your own pocket before insurance picks up costs. Most collision coverages apply to rental cars and the same deductible applies.
Liability coverage, which helps pay for damage to other people's property and medical bills, also applies to rental car accidents in most situations.

Two other optional insurance coverages might apply to your situation in a rental car accident:

Medical payments coverage may help reimburse your expenses related to doctor or hospital visits, ambulance transportation and surgery, among other things, for you and your passengers.
Personal injury protection (PIP), also known as no-fault insurance, is required in some states and not available in others. PIP also may cover medical expenses for you and your passengers.