Each nations four players represent the leader, defense minister, foreign minister, and science minister. There are phases for each turn where the counties plan together, then separate to conduct their roles: Foreign minister to the United Nations, science minister to a scientific conference, and defense minister to the world map. The nations leader flits around and makes deals, smooths tensions, talks to the press, and places their nations agents on the board.
I played the defense minister and was in control of the armed forces and space interceptors. The results were by the flip of a card from a common deck. It was quite tension filled as the aliens placed each ship and everyone had to choose whether to react to it. Decisions made could and did influence how the nations dealt with one another as they questioned allies and could create enemies. Spies were placed after the results of the battles, and they could disrupt alien influence, look for alien bases, steal technology from other nations, or anything they could explain with imagination and rationality.
It was played over seven hours and can take up to eight or end as early as six or sooner. As the narrative is up to the players terrible or wonderful things can happen.
Here is a 45 minute video from "Shit up and Sit Down" on playing an earlier version of the game for what it is like including a review. If one is organized in your city, I recommend it.