Wikipedia has classified "Person of Interest" as a "science fiction crime drama" - I kind of think they should have worked the word "detective" in there somewhere, but I guess "crime drama" covers it. The basic concept has "Harold Finch" (the pseudonym of a reclusive billionaire software programmer, played by Michael Emerson) having created a machine that identifies homicidal intent anywhere in the U.S. It was built only to find terrorists, but also finds many other crimes that are discarded because they're not terrorist action. Finch recruits homeless former special operations soldier John Reese (Jim Caviezel) to help him try to prevent these non-terrorist threats as the government is only dealing with the terrorist threats. But this puts them entirely outside the law, and in possession of a data source they can't even talk about. All they get is Social Security Numbers - and at that they don't know if the person is a target or a threat.
This is all set in current day New York City, and our two protagonists spend their time following people (in person and by electronic means) to determine what's happening in their lives and guessing at what's likely to happen to them. They tangle repeatedly with the police, and eventually recruit a couple members of the police force to assist them.
While Finch and Reese are reasonably charming characters (the police officers Carter and Fusco somewhat less so), and any individual episode is usually reasonably fun, I found the cumulative effect got tiresome and unbelievable. Examples include the amount of physical damage, including torture, that Reese accumulates. I'll believe it in one episode, but when it happens to him repeatedly, you know he'd eventually quit: there's only so much of that you can take. Or Carter and Fusco: sure, they can cover for "the man in the suit" in one episode, even two. But their constantly doing what he asks of them would have them fired (and probably jailed) in a matter of months.
I've watched a few episodes in the second season, and (as critical commentary suggested online), the storylines do seem to be somewhat better. But my complaints still stand, and I think my watching of the series is going to slow or stop.