It's a cop procedural but it's not a cop procedural. But the protagonists are indeed homicide detectives with the Seattle PD, investigating the disappearance (later, murder) of a young girl. The complexity of the murder mystery that spins out from this is too multifarious to adequately explain without spoilers, but it's masterful. And the way the case resolves is just so fitting, so true to itself and to, well, many a violent death. I was a little more lukewarm on the believability/necessity of some of the twists through the core of S1, but that is all 100% worth it, and S2 is strong throughout.
But I think my favorite writing scene in the whole show is the moment at the end of the pilot where they confirm the young girl's murder--you see it first-hand, from the perspective of the detectives. Then you see it from a greater physical distance, yet a closer emotional one, from the father. And you watch the mother react to his decontextualized screams of anguish via telephone, and then you see it in the terror and confusion of the family's two young sons, who are in the living room while their mother is on the phone, getting this news. Her death happens in layers and waves, and I can't believe more narratives haven't used this form (have they? I don't think they have), because it's just one of those things that is genuinely perfect storytelling.
Concepts that go into this salad include: complicated family ensembles, children and mourning/traumatic grief, adult mourning/traumatic grief, issues of class, issues of race/religion, political shenanigans, political campaigns, indigenous sovereignty, police corruption, the foster care system, land zoning laws, complicated romance, parent/child relationships, mob membership, psychological issues/trauma/damage, psychological treatment, stigmatization of psychological disorders/issues, the butterfly effect of violence/ambition, and so much more.
Also, I won't spoil you by saying who my favorite characters were, but JUST KNOW THAT I KNEW THEY WERE MY FAVORITES ALMOST FROM THEIR INTRODUCTION, BECAUSE THERE WAS JUST SOMETHING IN THEM THAT REALLY PINGED ME AND I REALLY LOVED. And then they turned out to be the major culprits. /O\ I'm not gonna say "bad guys," because that's explicitly counter to what The Killing is really about, but omg guys. Omg I know how to pick my favorites don't I. Because let me tell you, as much as that special something ~pinged my heart of hearts, I never once suspected them over the course of 26 goddamn episodes! O_o;;