If two triggered abilities trigger at the same time but are controlled by different players, in what order do they go on the stack?

When multiple triggered abilities trigger simultaneously, the game uses the Active Player, Non-Active Player (APNAP) rule to determine stack order. First, the active player (whose turn it is) chooses the order to place all of their triggered abilities on the stack. Then each non-active player, in turn order, does the same for their triggered abilities (CR 603.3b).

Because the stack is last-in, first-out, the abilities placed on the stack last will resolve first. This means the non-active player's abilities (placed on the stack last) will generally resolve before the active player's abilities, unless responses change the order.

Each player has full control over the relative ordering of their own simultaneous triggers — they choose the sequence. However, a player cannot choose the ordering of another player's triggers (CR 603.3b, CR 101.4).

Concrete example: It's your turn (you are the active player). Both you and your opponent control a creature with a 'whenever a creature enters the battlefield' trigger, and a creature enters. You put your trigger on the stack first, then your opponent puts theirs on top. Your opponent's trigger resolves first, then yours.

This rule applies regardless of how many triggers each player controls simultaneously — each player orders their own triggers as a group before the next player in turn order places theirs (CR 603.3b).