The world is pretty well fucked, with the exception of the USA. (And that's only because an idiot ran into the power source with a plane.)
You have two timelines going on at the same time: Red Alert 2 canon (General Carville dies, invasion of Moscow, yadda yadda), and expansion pack canon (moon bases, saving Microsoft, clone vats in Australia). This means that there are TWO Rachels running around. And yes, it's confusing.
Saving Microsoft (Massivesoft) also means Seattle is saved from Aagh Nuke.
The war (Red Alert 2 canon) ends during YR Mission 6. You have to save the peace treaty signing from Yuri. Lt. Eva gets mind-controlled into revealing the signing location. In return, she fucks royally with Yuri's plans and finds where HE's hiding once she's back to normal. (Yuri calls up the commander and taunts you, saying he might let you live as a zombie. Fat chance, Baldie.)
Allied campaign ends with Yuri locked up where he can never control people again. (He also gets laughed at by Allied soldiers. It is AWESOME.)
The timelines overwrite one another, and YR becomes the dominant canon. Carville lives, Yuri's invasion never happens,and the President is confused about why the general's on the phone and not dead. RA3 renders all of this moot, sadly. (Poor Einstein.)
In the Soviet missions, you get to fight dinosaurs and go to the moon. Let me reiterate that: you fight dinosaurs and go to the moon. AND you get to feed Yuri to a T-Rex. BADASS.