The basic storyline is that at the end of RA2, the Soviet Union is being overrun by the Allies, so the Soviets go back in time and whack out Albert Einstein, so that when they return to the present, the Soviets are in the process of finishing off Europe.
But in exchange, the Empire of the Rising Sun has risen in the east, and has begun a massive invasion of the Soviet Union.
I haven't begun exploring too far into the campaign yet, but you can co-op campaign missions with another player, and the skirmish mode is pretty freaking awesome.
I definitly recommend this game.