The character of Wolverine aka James Howlett aka Logan is a character that is definitely a breakout character among the X-Men. His past is long and storied (and overdone multiple times in the comics as well as in film) and many alternate futures see him as either an old, bitter man who has outlived everyone around him or a...actually, no, it's pretty much just that. Hence, we come to Old Man Logan, set in a dystopian future where the Red Skull has become President of the United States, the Abomination, Doctor Doom, and Magneto have likewise taken over portions of America. Naturally, being that FOX only had the rights to 50% of the aforementioned characters, some cutting down had to be done for this film.
I haven't read
Old Man Logan, but it seems a natural choice for Hugh Jackman's final (or so we're led to believe at the time of this writing) stab at the character he has played now for seventeen years. The entire film, in fact, feels like a good last hurrah for the character overall, whether he's further played by Jackman or not (and indeed, I do hope Wolverine fades a bit more into the background in years to come).