It's 2000-2500 years after some unspecified nuclear disaster occurred in the vicinity of Canterbury. And not your low-key Chernobyl-type event with a few abandoned towns and some radioactive sheep, either, this was your full utter devastation for hundreds of miles, not a living thing left unincinerated, the ground barren for generations kind of thing.
Humanity survives, as humanity will, though in somewhat reduced circumstances - civilisation has regressed to dark-ages semi-anarchy with small bands of scavengers scratching a living off the land and avoiding the jaws of the packs of marauding feral dogs. One of the things that they scavenge is the half-buried remnants of the old pre-apocalypse industrial landscape, huge metal and concrete structures whose purpose they have no idea of. The only entertainment is provided by travelling showmen who perform a sort of adapted Punch & Judy show ("The Eusa Show") incorporating garbled elements of the supposed events leading up to The Event.
Our eponymous hero decides he wants to see a bit more of the world after seeing his father killed while trying to extract some giant metal artifact from the mud and abandons the (relative) safety of his local community to wander the old grassed-over highways of Kent and try and make sense of things. As he does so he discovers more of the garbled history of pre-apocalypse England, but also the dangers that the insatiable human need to understand poses. To borrow a line from another post-apocalyptic novel, Stephen King's epic The Stand:
All of that stuff is lying around, waiting to be picked up.Sure enough there is a sort of miniature arms race going on as rival groups try to acquire sulphur to make rudimentary gunpowder - the other two ingredients being readily available. Given how utterly clueless these people are about proportions, safe ignition methods and the like, they are soon re-enacting The Event in miniature and wiping themselves out. Riddley takes it upon himself to take an updated version of The Eusa Show around in an attempt to prevent mankind from haphazardly working its way up to a point where it can once again destroy itself.
As it happens the plot here is, to a degree, secondary, which is just as well as not a huge amount actually happens. The most startling feature of Riddley Walker is the language in which it's written - since paper is a bit on the flammable side a disaster capable of rendering human flesh into two little bubbling pools of fat in a pair of shoes in a matter of nanoseconds is certainly going to destroy any written matter in the vicinity, and therefore the ability to read and write is a rare one, and even for those (like Riddley) who do possess it any notion of standard rules for spelling and grammar have gone out of the window, not that anyone has windows any more. Try this for size:
She said, 'Its some kynd of thing it aint us yet its in us. Its looking out thru our eye hoals … Its all 1 girt thing bigger nor the worl and lorn and loan and oansome, Tremmering it is and feart. It puts us on like we put on our cloes. Some times we dont fit. Some times it cant fynd the arm hoals and it tears us a part. I dont think I took all that much noatis of it when I ben yung. Now Im old I noatis it mor. It don't realy like to put me on no mor. Every morning I can feal how its tiret of me and readying to throw me a way. Iwl tel you some thing Riddley and keap this in memberment. Whatever it is we dont come naturel to it.'There's no getting away from the fact that this makes the book difficult to read, and requiring of a considerable investment of effort on behalf of the reader. This is not unique, of course, the most obvious other example being the Nadsat in Anthony Burgess' A Clockwork Orange. Other novels to dabble with this sort of thing include Iain M Banks' Feersum Endjinn (which I should say I've never read, but whose phonetic argot seems very Riddleyesque), and of course Nineteen Eighty-Four, though that restricted itself to some academic discussion of Newspeak rather than attempting to render any of the narrative in it.
The most obvious point of comparison is with Cormac McCarthy's The Road, Riddley Walker arguably being much the same story but with a much more immediately destructive initial event and 2000+ years of distance. In a way it's a more optimistic novel than The Road, though, as at least it's clear that organic life will survive, in whatever form, at least until humanity works out a way of obliterating itself again. The Road retains the implicit possibility that despite the commendable will to survive of the protagonists, the utter collapse of plant life may mean that humanity is fucked.
The other principal thing this has in common with The Road is that it is absolutely essential reading for anyone who is even slightly interested in modern fiction. Ignore the "science fiction" tag, as I think we've established that these words have no meaning. It's very different from the other two Hobans in this list, Come Dance With Me and Kleinzeit; those are charmingly playful, this is deadly serious.