Here is what I found on Wikipedia. I have not read every post on this thread, sorry if someone already put this up.
Deadly force, as defined by the United States Armed Forces, is the force which a person uses, causing—or that a person knows, or should know, would create a substantial risk of causing—death, serious bodily harm or injury. In most jurisdictions, the use of deadly force is justified only under conditions of extreme necessity as a last resort, when all lesser means have failed or cannot reasonably be employed.
Firearms, bladed weapons, explosives, and vehicles are among those weapons the use of which is considered deadly force. The use of non-weapons in an aggressive manner, such as a baseball bat or tire iron, may also be considered deadly force.
Deputy Sheriff with submachine gun
"Use of deadly force" is often granted to police officers when the person or persons in question are believed to be an immediate danger to people around them. For example, an armed man flaunting a firearm in a shopping mall without regard to the safety of those around him, and refusing or being unwilling to negotiate, would warrant usage of deadly force, as a means to protect others. The use of deadly force is also authorized when a person poses a significant threat to a law enforcement officer, usually when the officer is at risk of serious bodily injury or death. In the United States, this is governed by Tennessee v. Garner, (U.S. Supreme Court 1985) which said that "deadly force...may not be used unless necessary to prevent the escape and the officer has probable cause to believe that the suspect poses a significant threat of death or serious bodily harm to the officer or others." This case abolished the Fleeing felon rule where a fleeing felon who posed no immediate threat to society (e.g., a burglar) could be shot if they refused to halt.
However, in Graham v. Conner (U.S. Supreme Court 1989) the court expanded its definition to include "objective reasonableness" standard--not subjective as to what the officer's intent might have been--and it must be judged from the perspective of a reasonable officer at the scene--and its calculus must embody the fact that police officers are often forced to make split-second decisions about the amount of force necessary in a particular situation.
Most police agencies establish a use of force continuum and list deadly force as a force of last resort. With this model, agencies try to control excessive use of force. Nonetheless in the United States there are a high number of killings by law enforcement officers.
In the United States, a civilian may legally use deadly force when it is considered justifiable homicide, that is to say when the civilian feels that their own life, the lives of their family, or those around them are in legitimate and imminent danger.
In all advanced countries the law requires an investigation whenever a civilian or law enforcement officer uses deadly physical force that causes someone's death. This may include determining whether the officer's use of deadly physical force was appropriate under the relevant standards established. For example, in the United States an investigation is usually performed by a larger police agency and/or a civilian agency, such as a county prosecutor or State Attorney General. A report of the findings of such an investigation may be submitted for prosecution and made public.