So we managed to see this summer blockbuster-that-wasn't before it vanished from local cinemas. Avast: spoilers there be, below this line. Proceed with caution.
We pick up Han when he's a minor thief under the thumb of crime lord Lady Proxima on the ship-building planet of Corellia. (As you may remember, the Millennium Falcon was described as a "Corellian freighter" in the original movies.) Han has big plans, though: to escape Corellia and Proxima (not necessarily in that order) with his sweetie Qi'ra, get his own ship, become a pilot, and from there, make an honest independent living as a smuggler.
Things go awry. Many things. He worms his way into a band of thieves led by Woody Harrelson, their do-or-die mission to swipe a load of valuable hyperfuel for their employer, Paul Bettany. Things still go awry, and Han keeps getting further behind in his quest for independence.
Things we see: Han meeting Chewbacca; Han meeting Lando; Han (eventually) getting his hands on the Millennium Falcon; Han shooting first. We get additional confirmation of what we knew from past movies: Han likes to think he's an in-it-for-himself scoundrel, but at heart he's like a Chandler private eye: "Down these mean streets a man must go who is not himself mean, who is neither tarnished nor afraid. The detective in this kind of story must be such a man. He is the hero, he is everything. He must be a complete man and a common man and yet an unusual man. He must be, to use a rather weathered phrase, a man of honor, by instinct, by inevitability, without thought of it, and certainly without saying it. He must be the best man in his world and a good enough man for any world."
Real spoiler here: no Jabba. Hence there's a big gaping hole that could be (but probably won't be) filled by a second Solo movie, detailing what happens with Han and Qi'ra (now shown to be in thrall to Darth Maul) and Jabba on scenic Tatooine.