One of my all-time favourite alternate history (alt-hist) series is The Nantucket Trilogy by S.M. Stirling, also known as the Islander trilogy. The Nantucket/Islander books are: Island in The Sea of Time, Against the Tide of Years, and On the Oceans of Eternity.
The island of Nantucket, USA, is suddenly struck by a mysterious "Event," which separates it from its time and plunges it back, with its entire population of around 5,000 citizens (which includes tourists and vacationers) several thousands of years into the past. Specifically, the Bronze Age, or what's popularly identified as the age of Troy (as in the recent film of the same name).
Like all alt-Hist novels, Island in the Sea of Time doesn't dwell on how the Event was caused, or the scientific phenomenon behind it—even the Islanders never find out—but on the consequences of that Event and how the main characters deal with it.
And what fun it is!
First off, the Islanders are scared stiff at the challenges they're faced with, bereft of the 20th century and its luxuries, comforts, and support systems.
They're geographically still in continental America (or to be precise, just off the coast, since they're on an island—which is probably the reason why the Event cut them off)—but the land is a wilderness overrun by the ancestors of what they know as Native Americans.
After a period of struggling to come to terms with their new situation, during which phase different Islanders react in widely different ways—some commit suicide, others become lawless criminals, still others rise to the occasion and take charge of the crisis and restore order and sanity—they start to realize that they're here to stay. And since this is now their world, they had better start preparing and planning for the future. This means building ships and exploring the world, seeking out potential allies (and potential enemies), trading for things they need but don't possess, like certain crops and herbs and raw materials.
Inevitably, as in any end-of-the-world tale, two factions emerge, one faction the Good Guys, the other the Bad Guys. (It is an American novel, after all!)
The Bad Guys are led by Walker, who sees the opportunity to rule the whole world, using his superior technological knowledge, and his knowledge of warfare, to build an Empire. By the end of the first book, Walker and his team break away from the Islanders and start their own quest to build an Empire.
Over the next two books, this quest becomes a race to gain allies and conquer territories, using 20th-century weaponry and technology (and helped along by a knowledge of the history of the period) to build not one, but two separate American Empires across the otherwise barbaric world. (Boy, Bush would wet his pants in joy!)