An element the State has to prove in a DUI is that the accused was either driving or in "actual physical control" of the vehicle. Actual physical control sounds simple enough but the question of what is actual physical control has generated some interesting case law. Of note is that if the accused was not driving or the car was not moving, then the State can still prosecute a person having actual physical control.
In criminal cases, searches resulting from vehicle stops have been hotly litigated since the automobile became available to the public in mass. Since cars are mobile and not as private as your home, the Supreme Court has interpreted the constitution to afford vehicle searches and seizures less protection.