If a creature with annihilator attacks, does the defending player sacrifice permanents before or after blockers are declared?

Annihilator is a triggered ability that triggers when the creature attacks, meaning it triggers at the moment the creature is declared as an attacker (CR 702.87a). This places the trigger on the stack during the declare attackers step, right after attackers are declared.

Because the annihilator trigger goes on the stack during the declare attackers step, both players must pass priority and the trigger must fully resolve before the game advances to the declare blockers step. The defending player sacrifices the required number of permanents during this resolution (CR 702.87b).

This is significant because the defending player may be forced to sacrifice creatures they intended to use as blockers, or even lands they needed, before they ever get the chance to declare any blockers.

Example: Your opponent attacks with Emrakul, the Aeons Torn (Annihilator 6). The annihilator trigger goes on the stack. Your opponent passes priority, you pass priority, and the trigger resolves — you must sacrifice 6 permanents immediately. Only after all of this does the game move to the declare blockers step, where you must deal with a 15/15 flying, trample creature with whatever remains.

Relevant rules: CR 702.87a defines the annihilator trigger timing, CR 509.1 (declare attackers step) and CR 509.4 (priority after attackers) confirm the trigger resolves before CR 509.5/510 (declare blockers step).