Most insurance companies will have a notice about using aftermarket parts as oppose to OEM (Original Equipment Manufacturer). Parts made by after market companies tend to be cheaper than OEM. Insurance companies have this on their policies because it allows them to save money on the estimates.
Most of the general complaints about aftermarket parts consist of the part itself not fitting well on the vehicle. Many shops simply refuse to to utilize these parts for that simple reason.
Check Your Policy
Most companies will have a section on the policy booklet noting the usage of aftermarket parts. Some companies will use aftermarket parts when a vehicle reaches a certain age.
Insurance company A will use aftermarket parts when a vehicle reaches one year old or 12,000 miles. It is 2011 and you have a 2010 Nissan Cube with 14,000 miles. They will use aftermarket parts on your vehicle while estimating your car.
What You Can Do
Now no need to jump in panic when you see aftermarket parts listed on the estimate. Insurance companies like to keep their customers happy (I hope). If the part shows an obvious defect they will generally pay for an OEM part in place of it.