If you've ever heard of the "many worlds theory," the idea that any event that could have turned out more than one way creates a split in the universe so that the event turns out each of the possible ways, then you know the basis of a subgenre of science fiction folks call alternate history. You could just see alternate histories as fantasies with no particular basis in reality, but the many worlds theory, which came from quantum theory, is the basis for these stories.
Even some time travel stories tackle it: you go back in time, accidentally make a consequential change, and the future you return to is different. What happened to the future you came from? It's probably still there. You just can't reach it anymore, unless you travel even further back in time to prevent the first change.
One fairly rare take on the many worlds is the ability to travel laterally between them. Instead of flying to the stars to find a new planet, you travel from our planet to a probabilistic neighbor. It's got everything Earth has, except people. No pollution, no overcrowding, all that good stuff. So far a few stories have been written considering this idea, but most if not all of them are short story treatments. I know of none that explored the subject as thoroughly as Pratchett and Baxter do in The Long Earth and The Long War.
Some time in the near future the world changes. A scientist posts plans on the internet for building a stepping box, a simple device, apparently powered by a potato, which allows the wearer to step from this world into an alternate world. The worlds stretch out in two directions, for infinity, it seems, and at first appear to be completely devoid of any intelligent life, though in other respects life flourishes on most of them.
The stories' main character, Joshua Valienté, accompanied by a computerized simulation of a Tibetan mechanic named Lobsang sets out to explore the Long Earth, and perhaps discover its purpose. The fairly mundane task of exploration is leavened by a continuous conflict between Joshua and Lobsang arising from Joshua's distrust of this machine that appears to have an indecent amount of power over the lives of people. The story finishes with a perhaps predictable event that has nothing to do with the main plot, but that's actually OK since it leads to the sequel.
The sequel takes place a couple of decades later. Human prejudices against trolls, gorilla-like intelligent beings who live in the Long Earth, naturally stepping between worlds, are resulting in the withdrawal of the trolls from most places in the Long Earth. Sensing a threatening war between humans and non-humans, Joshua and his computerized friend set out again to see if they can broker a treaty. This story also has enough unfinished business at the end that it's obvious there's going to be a sequel - The Long Mars.
Which I haven't read. Yet.
Anyway, stylistically both books show the hallmarks of a collaboration. Both Baxter and Pratchett are stylistically competent, as is this book. The prose doesn't evoke either author's distinctive style, though both authors toss in occasional sly references to their own works - just not anything that disrupts the flow of the narrative itself. The result is a consistent and even flow of narrative that is easy on the mental ear.
There is a large number of characters who make their appearances as the plot advances. Each get a fair amount of time for development, and in the end, paradoxically almost, the one character that remains a cypher is Lobsang, who plays the role of cat's paw in both books. Instead of developing as a central character, the AI acts as a foil against which many of the other characters measure themselves. Since the books are not actually about computerized intelligences, that's as it should be.
Pratchett and Baxter include many different worlds in the story. I enjoyed the descriptions of the varied animals and environments found on the Long Earth, even the idea of Jokers, places that are unusually different from the surrounding Earths, was a great idea. While the story starts with the appearance that humanity is alone on the Long Earth, there are hints early on that we've got company. The second book even presents a scientific rational for this state of affairs. And of course stepping itself has a number of limitations, which are addressed in a variety of ways.
The books are not the usual thing to expect from either author. It might be a good idea to approach the books while pretending you had read nothing by either author before. The books deserve to be seen in their own light.
Overall I strongly recommend the stories.