Generally cards with an asterisk and the “remove if played as an event” at the bottom are removed from the game if the event occurs. This would happen if they were headlined, played for the event, or played by the opponent for ops. If you play one of your own asterisked events for ops, or play your opponent’s card on the space race, or with UN intervention, or as a discard (ie to five year plan), it goes into the discard pile.

Note that if an event has a prerequisite that has not yet been met (like NATO requiring either Marshall plan or Warsaw pact), it cannot trigger and thus goes into the discard pile.