Wikipedia calls this a "mystery-crime thriller neo-noir action comedy film" - I would have watched it just for that genre definition.
Ryan Gosling plays Holland March, a chronically sleazy private detective who investigates cases that often exist only in the heads of his clients. He's aware of this, but generally just takes their money. Russell Crowe is thug-for-hire Jackson Healy, going around beating people up when he's paid to do so. A day or so after breaking March's arm for investigating the disappearance of Amelia Kuttner, he has a change of heart and returns to March to hire him to continue looking for her.
This is the basic plot outline. And the plot's not too bad, but also not really the point. That's more about how these two ethically challenged and quirky individuals deal with trying to do the right thing and with each other. Many comedies make characters act contrary to their own behaviour just to be humorous, and that tends to really mess up my suspension-of-disbelief and ruin the movie for me - this movie doesn't do that. Staying true to the entertaining characters they've written and putting them into awkward situations leads to a howlingly funny movie that I really enjoyed.