Generally, the insurance company for the person who caused the accident will pay to fix or replace your car, pay storage and towing, as well as loss of use (rental fees) and diminished value. However, the insurance company for the person at fault will want to conduct and investigation into the facts and may take weeks to finally decide to repair or replace your vehicle. Often, the fastest way to get back on the road is to take advantage of your own car insurance coverage to repair or replace the vehicle and provide the rental and cover the other costs. Your insurance will generally pay out your claim much faster, though you may have to pay or reduce the payment they make by your deductible. Often, when this is done, your insurance company will work independently to get paid back by the other persons insurance company and get your deductible back.