The insurance company of the person who hit you will pay to have your vehicle fixed. If their insurance company challenges liability (whose fault the accident is), they may not pay for your car right away. If this is the case and you have collision coverage on your policy, you may want to turn to your own insurance company. If you do this, you will have to pay your deductible. Your insurance company then would attempt to collect the deductible back from the at-fault party’s insurance company.