Compensation will typically come from the insurance company of the at-fault driver. Collecting can become complicated if the at-fault driver does not carry insurance.
In the state of Washington, a motorist is not required to carry uninsured or underinsured motorist coverage, but every driver should. If you find yourself in an accident with an uninsured motorist, you likely will not be able to get any compensation from them by suing them.
Most drivers that do not carry insurance do not have enough assets to provide damages. If you have coverage for an uninsured motorist, then your insurance company should cover your damages.