I find it interesting that Terry Pratchett waited until he developed Alzheimer's to delve into writing non-Discworld books. OK, yeah, it was Good Omens that got me reading Pratchett and Gaiman in the first place, but that was a one shot. With "The Long War" he and Stephen Baxter have turned their collaboration into a series. Since Pratchett can't read or write anymore it amazes me how productive he's been.
In the Long Earth books someone figured out how to step between alternate Earths using a device that anyone can build from parts they picked up at Radio Shack. Which these days means it was probably a mobile phone and remote control truck. Anyway, as of The Long War, none of these Earths have Humans on them. Just untouched wilderness. You could spend the rest of your life moving between worlds hunting and gathering and living well on the resources at hand. And many people do. Billions of people have made like settlers and headed off across the alternative worlds to start new lives and new colonies.
Along the way they've met Trolls who can step across worlds naturally and love to be well treated slave labor. There's other intelligent life, too, but they're not important at the moment. Not everyone treats the Trolls well. Enough people don't that the Trolls have started leaving all the known Earths.
Earth Datum (or Earth Prime or Original Earth) is getting on reasonably well mining the neighboring Earths for resources. But, even with the drop in price the economy has pretty much been shot to hell by having a great whopping chunk of it's population head off across reality. And you know what kinds of politicians rise in those kinds of environments. Those who have left are the enemy and America Datum needs to assert it's control and dominance over those who have moved to alternate Americas for the glory and betterment of AMERICA! And, yeah, a few hundred thousand Earths away they're not sure why they need to pay taxes to distant people who hate them. But those from the Datum have no clue how things operate outside of their home world.
The title "Long War" implies a lot more fighting than actually occurs in this book. A few intelligent people in military command positions manage to keep the idiocy of politicians, home bound bigots, and violence loving troops from turning violent when they finally encounter the separatists. And things sort out with the Trolls pretty well. The most violence is when a race known as Beagles capture one of the main characters and hunt him for sport.
Really, this is an expansion on "The Long Earth". It's further exploration of the world(s) with more emphasis on the life, the politics, and overall development of life in this reality.
It also talks more about The Gap. The Gap is a series of realities where Earth isn't there. A space program pops up on the edge of The Gap and starts using it to explore. Presumably, that's the jumping off point for the next book "The Long Mars".
If you're looking for something like Pratchett's other work, this isn't going to be it. This isn't Discworld. This isn't Good Omens. This is serious science fiction in which those who know his work can still see Pratchett's thinking in play. I should warn you, this is a long (no pun intended) book that took me quite awhile to read.