In A History of Violence, small-town perfect father Tom Stall gets accosted by gangsters who think he's the gangster Joey Cusack. Is he? Of course he is!
Maybe, in a Hitchcock film, the protagonist might have a chance to be the wrong man; but in just about any other film, we kind of know that Tom Stall really used to be Joey Cusack. So there's not a lot of mystery about his identity: he used to be a killer and a gangster. So how does the film keep our attention with this big mystery more-or-less taken off the table?
Primarily, there's the suspense and the menace of the situation. We know he's the killer Joey Cusack--so now we nervously wait for the situation to shake out, for it to ripple through his perfect life. Which is why we spend so long seeing the world as it is before the trouble starts, sometimes in an almost over-egged way.
For instance, when little girl Stall has a nightmare, dad comes in to comfort her. Aw, perfect dad! Then brother Jack comes in to comfort her. Aw, perfect siblings! Then mom comes in--and everything is perfect. The son's biggest problem seems to be playing baseball in gym class, about which dad gives him some advice, which turns out to be useful when Jack catches the ball and wins the game. Sure, that gets him into trouble with the school bully--but Jack defuses that situation also. Dad faces the problem of litter outside his diner; inside his diner, his cook and his customers all get along. There aren't many problems in the Stall world and every problem is manageable.
Also, there's the scene where Tom Stall and his wife have sex with her wearing her teenage cheerleader outfit, since "they never got to be teenagers together."
All this "perfect Stall-world" would almost be boring if the movie didn't start by introducing us to two wandering killers. Again, this scene is structured around suspense and delay: just as we saw the angry bully approach Jack, so here we hear one say that he "had a little trouble with the maid"--and it's only a little later that we see what this means.
So when these guys show up in Stall-world, we know how much the Stalls have to lose--and we have to wait to see how it's going to blow-up when they arrive in town after being gone for so long. (Bonus: they are driving in a different car, a nod to how they've stolen and killed their way across the state, I think.)
One of my favorite little sequences similarly uses suspense and delay--playing with what we can see and can't: when Tom worries that some gangsters are going to his house, he runs--limping--towards his house (delay #1). He calls his wife, who doesn't pick-up at first (delay #2). She eventually picks up and gets the shotgun ready, just in time for her to point the gun at Tom when he runs in. Only then do we see that Jack Stall is sitting at the kitchen table eating cereal and watching all this, which is an intense moment for him--and for us since we see that he had no idea what's going on. Then while mom goes to take care of daughter, Tom puts the shotgun down on a table--and the camera lingers for a moment before panning off of it, just to remind us that there is a loaded shotgun in the room--and that we can't see it when we turn away. I remember sitting in the movie theater, trying to move the film camera with my mind to show me the shotgun.
Now, A History of Violence uses delay and suspense a lot, but it also doesn't mind skipping some transitional moments. For instance, Tom Stall gets wounded twice in the movie and in the next scene, he's at the hospital confronting the emotional/character fall-out of the issue. We never waste time seeing anyone call the ambulance or see Tom get doctored. It would be a big waste to see that: we don't care about Tom's relationship with his doctor, only his relationship to his wife and kids.
Similarly, most of the violence here happens quickly and messily, since the violence is only interesting insofar as it affects Tom's relationships.