I got this somewhat randomly several years back in preparation for the WorldCon panel I chaired with Turtledove as one of the participants. I didn't manage to read it then, though; bounced off the first couple of chapters. I have now struggled through it as part of my ongoing programme of clearing my backlog of unread books.
The book is, it turns out, the third of a trilogy about an alternate history war ending in 1917, where the US and Germany are fighting a bitter trench combat against Britain/Canada, the Confederate States of America fifty years after their victory in the War of Secession, and France. All the action takes place on or near the North American continent, so the fact that I didn't read it before our panel on the future of Europe is no great loss. The major one of the "Breakthroughs" of the title is the penetration of Confederate lines on the Kentucky/Tennessee front by the US army's new battle machines (known as "barrels" rather than "tanks" in this world), under the command of septuagenarian George Armstrong Custer, as a result of which the Confederate front collapses, the US re-occupies Washington, annexes chunks of Canada and declares Quebec independent, and the war and the book both end.
Turtledove has about a dozen viewpoint characters, telling the story from the point of view of the military and civilians affected by the war. US president Teddy Roosevelt pops into the narrative now and then, and the defeated CSA president appears at the end, but on the whole this is the story of the little people. It is detailed and well worked out, but didn't quite grab me as much as I was hoping. I very much enjoyed Turtledove's Hugo-winning novella "Down in the Bottomlands", and wonder if the discipline of the shorter form enables him to concentrate quality rather better than in a trilogy of 650-page books.