You can file a claim through your own company and have them file against the offender's insurance. In my case, Allstate filing on my behalf to Farmers. Basically, I have to pay my deductible up front but will be reimbursed for that when Farmer's comes through.
They will recommend a very lame body shop. You have the right to use whatever body shop you want. Any use of the words "Service King", "Sterling" or similar such chain body shops should offend you. I'm told they "tend to use cheap Korean and/or junk yard replacement parts" even when said parts are not bolt-on parts. They also pay their people just over half the wages of a reputable shop. The initial recommendation I got from Allstate was to use a junk yard quarter-panel, which would have to have spot welds drilled through and then be pried off of the donor car. After all that bending, the metal is typically fux0red. You typically have a clause in your insurance policy that allows you to use Original Equipment (OE or OEM) parts where applicable. I'm told this is key to having a good repair and it's up to the keen eye at your body shop to demand this level of quality.
They seriously low-ball you up front. I was told that over 60% of people who file a claim don't actually get their car fixed. I was cut a check for $2600 to fix my car, but upon initial inspection at the body shop, they said it would be closer to $4k. Insurance has a mechanism for this: the supplemental claim. It's up to your body shop to file this supplemental claim to get the correct parts to fix your car. Sterling, Service King, etc, are less likely to file such a supplemental claim, which is why the insurance companies love them. They'll typically accept a low-ball bid and do everything they can to meet that low budget - even if that means your car is fugly after the repair.
Talking to the guys at Details, Ltd in Addison really enlightened me and left me feeling like I had my car at the right place. After telling the insurance adjuster where I was taking it, he concurred that that was one of the best body shops in town.