Driving under the influence. Can either refer to driving under the influence of alcohol, driving under the influence of drugs, or driving under the influence of a combination of liquor and drugs. This is the most widely used acronym for drunk driving cases. The standard for what it means to be under the influence will vary from state to state. It is important to contact a lawyer in your area that knows DUI law if you have been accused of DUI or a related drunk driving offense.