The trajectory of Saints Row has been watching your player character, "The Boss," fail upwards. He (or she) is not particularly clever or skilled at anything besides causing havoc, but has ended every game at a higher level of power and influence.
In Saints Row 4, The Boss has now risen to the level of President of the United States, and of course, it's not going particularly well. The presidential premise seems to fall by the wayside once aliens invade and trap humans in a virtual prison, but I don't think it was just a silly throw-away idea. It pronounces upfront that your character is actually kind of a boorish jerk. This is an ensemble production, and trouble follows when the Boss forgets that he needs the Saints more than they need him.
That's probably why so much of the time is focused on rescuing and then fostering relationships with your "Homies." Oddly, the end result is an experience that draws many similarities to Mass Effect 2. The bulk of missions involve either rescuing your Saints crew from their own mind-prisons, or helping them wrap up loose ends in "Loyalty" missions. The recruitment missions are especially well-differentiated, predicated on the notion that the alien Emperor Zinyak has constructed a custom reality to trap each Saint.
Once rescued, you can even "Romance" the crew, and each of the vignettes is played for laughs. The romance options are admirably gender neutral, just like the personality of the Boss him- or herself. Only Keith David turned down my Boss--that scoundrel!
Being trapped in a virtualized Steelport is the perfect excuse to introduce a key new gameplay element: superpowers. Immediately, Saints Row 4 sheds its "GTA clone" legacy, by making cars wholly unnecessary: the first powers you earn are super versions of dashing and jumping, letting you traverse the world in a completely new way. As a superhero president, the sense of agility and speed the game endowed was wonderfully empowering, even if some of the later powers are a bit disappointing.
Of course, being an open world, Steelport needs to offer players a variety of activities. Saints Row 4 impresses, although some of them (like Fraud or Mayhem) are familiar from previous games. Secondary objectives are also the primary way to gather Cache for upgrades. Saints Row 4 stacks upgrade systems atop upgrade systems, and it's just on the hair's width from being overcomplicated. You can upgrade yourself and your equipment using Cache, or your superpowers using Data Clusters. In fact, the Clusters are are so numerous that obsessive collectors might have a hard time making it to the next mission objective in a timely manner, as glowing blue baubles tempt exploration around every nook.
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As a franchise, Saints Row has never been as refined as some of its competitors, and that hasn't changed. It's still a B-tier open world game, and while that grants it some lovable qualities, the world and characters do lack some physical presence. The rag-doll effect when the Boss is knocked down looks particularly old-fashioned, which I found strangely charming. On Xbox 360, SR4 also suffered the occasional stuttering during some large-scale action sequences.
But what it lacks in technical prowess and budget, Volition makes up with humor. It can be a little hit-or-miss at times, but the hits keep coming when the game relies more on the studio's own sense of comedic timing than a referential bit. The writing is still a standout, with laughs coming within seconds of starting the game--and the less said to spoil the punchlines, the better.
Saints Row 4 doesn't do anything particularly new or revolutionary, and it certainly won't be remembered as a generation- or even genre-defining event. But it is a thoroughly well-executed absurd empowerment fantasy, and a fond farewell to its peanut gallery. This might not be the game to evoke essays on meaning and artistry, but I haven't had more fun this year. 
This review is based on early retail Xbox 360 code provided by the publisher. Saints Row IV will be available at retail on PS3 and Xbox 360. It will also be available digitally on PC on August 20th for $49.99. The game is rated M.