The term 'action movie' is a slippery one, but I have a few guidelines. I generally curtail the term to non-science fiction films from the pre-CGI epoch, which contain a law enforcement angle. Therefore, some titles that fit into my action genre would be Die Hard, Blue Steel, Cobra, and Point Break. There are surprisingly few directors who can bring artistry, or at least meticulous craftsmanship to an action movie of this stripe. If I had to come up with a list on the spot there would only be a handful of names, but I'm sure the list would include John McTiernan, Kathryn Bigelow, and the recently deceased George P. Cosmatos.
Kathryn Bigelow started out in the painting world, and was an assistant to the sculptor Vito Acconci before making her filmmaking bones at the University of Jim Cameron, which must be more interesting than shelling out film school tuition. She was married to Cameron briefly and used a story he wrote to form the basis of her ambitious 1995 film Strange Days. The two share a lot in common stylistically, and she, like him, is refreshingly un-prolific, good at casting, and willing to go to the wall to get the shot.