This is the latest novel from Michael Chabon, a fantastically gifted storyteller and writer. It's been nominated for both an Edgar award (given to mysteries) and a Nebula award (given to science fiction). It's just a plain old good book, though, and Chabon should be honored to have both genres fighting over its ownership.
What makes it at least vaguely SF: it's set in an alternate history in which millions of Jews were accepted as refugees by the pre-WW2 US. Good news: the Holocaust "only" kills two million; bad news: the refugees settle in and around Sitka, Alaska, without full citizenship. When the novel opens in the roughly-present-day, America is about to take back even that stingy offer, and yet another Jewish diaspora is threatened.
What makes it a mystery: the hero is a down-on-his-luck police detective named Meyer Landsman. He lives in the downscale Hotel Zamenhof, where he "drinks to medicate himself, tuning the tubes and crystals of his moods with a crude hammer of hundred-proof plum brandy." One night the manager summons him to the room of heroin addict "Emmanuel Lasker", who's been professionally shot in the back of the head. Meyer's intrigued by a chess set, poised in midgame. Even though (seemingly) nobody really cares about a dead junkie, Meyer's still a good detective and is soon enmeshed in a thicket of conspiracy, etc.
Chabon gives Meyer good wisecracking dialogue in the tradition of hardboiled fiction; he does a fantastic job of seasoning it with weary Jewish ruefulness.
Should you undertake this 400+ page reading project, it helps to pay attention to what initially seem to be colorful people and events that seem only to be adding atmosphere and character development; many turn out to be integral to the plot. (And you don't have to have a familiarity with Jewish custom and the Yiddish language to get through it, but it would probably help.)
The book's Wikipedia entry says there are plans in the way to make The Yiddish Policemen's Union into a movie, with the Coen brothers directing. That would be awesome. The article also summarizes what the book says (and sometimes only hints at) how the alternate history differs from ours. But—wait a minute—also be careful about reading the entry before you read the book since it summarizes the entire plot all the way to the end.