Every character in an opponent's Zone of Control and aware of it is considered Engaged. He cannot concentrate on his surroundings because he is busy not being struck down.
During any Turn a character starts Engaged, he doesn't receive a Complex Action. He cannot actively Evade missiles.
In order to disengage, he can either use the Maneuver Melee Action to leave the opponent's Zone of Control, or use Movement to leave and incur an Attack of Opportunity.
Engaged status doesn't need to be marked as it's determined by the position on the battlefield.