A little something I've been doing a bit on ever now and then. Had a vague idea for a sort of WorldWar-Star Trek crossover scenario, and a map emerged.
Some background changes: the Race seems sort of the “standard model” for alien races in their universe, seeing that the first two species they encountered were more like them in behavior than humans. Since that isn’t the case in the Star Trek universe, the human race is the first alien race they’ve run into: given that before later ret-cons trips in the thousands of light years were not unusual in Star Trek, I’m assuming alien species are more widely separated than in Turtledove’s books. The Race simply assumed that human technological progress would take place at a pace not too dissimilar from theirs, and accordingly took just as long to get an expedition going. (They have established colonies on several desert worlds with no native sapients).
There were no Eugenics wars (which given the timescale involved, never made any sense except as a result of meddling time travelers or aliens – have they come up with a new explanation for it? I haven’t followed Star Trek very closely since watching the first two episodes of “Enterprise” and being rather unimpressed). However, without a WWIII and a strong incentive to discover FTL, the warp drive was discovered nearly a generation before Cochrane did in the Star Trek timeline. Race intelligence discovered US plans to build a massive starship to carry out an expedition against the Race homeworld, and in a panic prepared to carry out a full end-of-the-world attack against the human Not-Empires.
It was at this point that the Vulcans intervened and gave everyone a good talking to. The Vulcans defused the crisis by making it clear they would not tolerate anyone committing genocide on anyone else, and gave the Race an FTL drive of their own. They also negotiated a peace treaty between the Race and the human nations in which the Race withdrew from most of its conquests to the core desert areas from which they had already been expelling rebellious humans for a couple generations. (Some bribes of high technology helped seal the deal).
Forty years later, the Race has largely “ethnically cleansed’ its territories, which are now over 95% Lizard. The Race is having some definite problems in this new era, having to run as fast as it can to just keep up with the Terrans technologically as they assimilate advanced alien science imported from all over the local galactic neighborhood (not to mention that they are suffering from severe psychological shock at the discovery that humans are the Standard Model for alien species: this has brought on somewhat of a religious crisis.) With the warp drive to rapidly bring in new settlers and the aid of Vulcan technology (the Vulcans are quite experienced in desert living) they have increased the population of their settlement area to several hundred millions: however, the always slow and cautious Imperial government has so far established only one new planetary colony, while the humans have established footholds in several dozen uninhabited systems.
The bulk of humanity is united in the still fairly loose Terran Confederation, headed by the US, a largely post-ideological and fairly democratic USSR (although still more socialistic than the US: the notion of a planned economy was given a boost in the arm by the fact that the rational and super-computer equipped Vulcans do manage the “commanding heights” of their economy for the common good ), and Japan, whose subjects no longer feared being swallowed by the race and whose younger generation felt uninterested in spending their lives terrorizing aforesaid subject peoples when the stars beckoned. The Confederation has close ties to the Vulcans and largely consists of democratic nations.
With the notion of humans as a united species in a universe filled with advanced aliens races has come some enthusiasm for the idea of political unification and federation, and while the Canadians are still surprisingly disinterested in joining the US, several large political unions have arisen in the wake of the withdrawal of the Race, from the Bolivarian Union to the Swahili Federation. Bangladesh has remained part of India, and Argentina has absorbed Uruguay (it also gained the Race-held Malvinas or Falklands, which annoys the Brits a little). On the other hand, fragmentation has occurred in several places as a result of independence: most of the population of Ethiopia had no desire to end up back in a unitary state run by an ethnic minority, Spain failed to retain a unified identity, and the rather different historical trajectories of Race-ruled north Vietnam and the South have so far baffled efforts to find a formula for reunification.
However, not all of humanity is part of the Confederation, or happy with the political arrangement thereof.
The Chinese, mixing ideas from Communism, old-style Chinese ideas on righteous government and Confucianism, and admiration of the Vulcans which had brought about their liberation, ended up forming a type of technocratic, paternalistic “science dictatorship” based, supposedly, on “pure reason” (the Vulcans disavow any relationship between their form of government and the Chinese). Given human nature, it’s really not all that rational, but of course those saying so are by definition irrational. The energetic dictator of the Congo-Angola region is a devotee of technocracy himself, if only because he needs the alliance to maintain his hold on power.
The Chinese maintain their independence from the Confederation, but generally remain on cordial terms with it, in spite of their agreement with the Race on the irrationality of “snout-counting” as a means of government. They think much less of the Islamic Alliance nations.
The Islamic alliance arose from the firm (and not entirely unjustified) Arab and Iranian belief that they had been thrown under the bus for the sake of world peace. Over 150 million people of Arab descent live outside of what they consider to be their homelands, the majority resettled by the Race in other parts of Africa, Latin America, and India.  This huge and unhappy Diaspora forms the ideological base for the United Islam movement that that has emerged in the last few decades, formed the Afro-Arabic Union along the southern border of Race territory in Africa, and prompted NW India to break away and join with the Afghans to create the Suristan Republic. United Islam has so far not been able to agree whether Khartoum or Multan should be the capital of World Islam, or exactly how the expulsion of the Race from the Middle East is supposed to occur, but they agree that they will not rest until the area is once again Muslim.
Then of course there is the Third Reich, which will not submit cheerfully to the leadership of a world union full of untermensch. After a century and a half of state-imposed pro-reproduction policies and assimilatory policies, there are some 360 million people in the Reich proper, and the north Italians, Croats and Czechs have been largely assimilated. (Much of the anti-Slavic rhetoric has been dropped, although black Africans and Jews are still considered racially inferior). The satellite states of Romania, Bulgaria and Hungary are a bit of a problem: although tightly controlled and integrated into the Reich economy, direct absorption does not seem to be on the menu anytime soon (there are still south Italians and Greeks and Albanians, and they are troublesome enough as it is) and the Reich’s security forces are stretched tight as it is. Meanwhile, they are struggling to build a space empire of their own with rather limited resources – but there must be no flagging in discipline. After all, with sufficient Will, anything is possible!
Not that manpower shortages and insufficient determination are the biggest problem facing the Reich. Although the Eugenics Wars of OTL did not take place, the Germans have been trying to engineer – or build – a better German for some time, and have had some success. A conflict looms between the mostly old-style human leadership and a crop of genetically manipulated, upgraded young Germans with their own plans for how to run the Reich…
The Jews, which prospered for a while in Race-run Palestine, are again in exile from the Holy Land. Still, they persist, and flourish, in the USSR, the US and even Poland: perhaps not this year, perhaps not this century, but they still say “next year in Jerusalem.” (Which city, being holy to several religious traditions, was established as an “open city”, Race-managed but open to visitors and settlers from around the world. It is currently rather crowded and requires a major Race military presence to maintain order between squabbling Christians, Jews and Muslims).
Also an internationalized area is the Amazon basin. Having never encountered anything like this extraordinary wealth of life on the dry, desert worlds they preferred, fascinated Race scientists successfully lobbied to keep this area free of settlement and exploitation, a status maintained (with some prodding from environment-conscious Vulcans) post Race withdrawal. Extreme piss-off with the loss of national territory is one of the major reasons for Brazil going fascist (Sri Lanka is an odder case).
France, due to the Germans squealing like pigs in a slaughterhouse at the idea of “encirclement”, has been neutralized, and after a century of first German and then Race occupation, is happy enough to be independent and cultivating its own gardens without worrying about world politics.
 On the other hand, there's also a lot of capitalism on Vulcan: Vulcans, after all, are genuine rational choosers.
 There are some 30 million Arabs and Iranians living in the US, USSR and the Japanese Empire, where they form a generally loudly anti-Race lobby.