A book series by AH veteran Harry Turtledove. The basic concept of this scenario is that an alien race invades the Earth in the middle of World War Two (May 1942). The aliens, known only as The Race, have already conquered two other planets and are confident of their victory, as they have sensor data of the Earth from 'only' 800 years before and are sure it cannot have progressed much since then. They have a rude awakening when they learn that humans advance a lot faster than they do, taking risks and ignoring the potential cultural impact before acting.
The first four books deal with the initial war, which ends in a stalemate with five major human powers - the United States, the Soviet Union, Nazi Germany, Britain and Japan - plus a host of minor island nations and Canada remaining independent, while the rest of the world becomes part of the Race's Empire. The Colonisation trilogy, set 20 years later, follows with the arrival of colonists from the Race's homeworld and a nuclear war between the Race and the Nazis. Finally, the standalone book 'Homeward Bound' completes the series with humans travelling to the Race's homeworld (“Home”) and finally surpassing the Race's level of technology.
Criticism of the series tends to claim that the writing quality deteriorated over the course of the series, with books becoming longer and more padded. The first book, “In the Balance”, is considered by many to be the best. Some people dislike the concept of the Race, with its reptilian focus on doing things slow and steady, its generic emperor-worship religion and its desire to incorporate everywhere into its Empire.
The Race come from a planet they name, simply, Home, orbiting the red star epsilon Eridani. It is a desert world whose year is about one-half of Earth's. Home was united 25,000 (Earth) years ago and has since been ruled by the same line of Emperors, though usually the Race do not reckon descent and family of any importance (possibly an inconsistency). They are normally inert to sexual desire but go into a periodic breeding season, not retaining any connection to sexual partners thereafter. They do not track which hatchlings come from which eggs and thus members of the Race are not raised by their relatives and have no concept of family. This caused friction with humans.
The other two races in the Empire are the Rabotevs and Hallessi (the Race names for their stars) who are similar reptilian races, hence why the Race were so taken aback that humans were different. The Race named the Sun Tosev, the Earth Tosev 3, and humans Tosevites. Their common nickname for humans is 'Big Uglies', as the Race are rather shorter, but humans call them 'Lizards'.
Religiously speaking, the Race venerates their Emperor and the spirits of Emperors past, believing they will serve them in the afterlife. They consider all else superstition.
Their military technology upon reaching Earth was about that of the state of the art when Turtledove wrote the first book (1994) save that they also had fusion-drive spacecraft. They have had the same military technology, unchanged, for millennia. Although the Race had a significant technological advantage over even the best armies of 1942, humans were able to out-produce them and, significantly, learn, improve and adapt their weapons and strategies at a rate that alarmed the Race. What ultimately ended the first war, however, was when three human powers - the Americans, Soviets and Nazis - all developed nuclear weapons and used them. The Race's fleetlord, Atvar, was unwilling to use more than a few of his own bombs, as this would render the planet uninhabitable for the colonists following him. Thus it was divided.
The Race's alien-ness is emphasised with various terms for military items: tanks are landcruisers, planes are killercraft, and “-man” is replaced by “-male” (e.g. wingmale, infantrymale). The Race did not have any concept of a navy before reaching Earth due to Home only having small seas. Their military or civil rank is indicated by a pattern of body paint, and they wear little other clothing.