Does a creature that attacks become tapped immediately or only after the declare attackers step?

When a player declares attackers, tapping the attacking creatures (those without vigilance) is part of the declaration process itself. According to CR 508.1f, as part of declaring attackers, the active player simultaneously taps all attacking creatures that don't have vigilance. This happens as a single, simultaneous action during the Declare Attackers Step.

This means the creatures are already tapped by the time any player receives priority in that step. After the declarations are made and the associated costs/actions (including tapping) are completed, the game checks state-based actions and then players receive priority — but the creatures are already tapped at that point (CR 508.1, 508.2).

Vigilance is the keyword ability that modifies this rule: a creature with vigilance doesn't tap when it attacks (CR 702.20b). Without vigilance, tapping is mandatory and simultaneous with the declaration.

Concrete example: You attack with a Grizzly Bears (a vanilla 2/2). The moment you declare it as an attacker in the Declare Attackers Step, it taps immediately as part of that declaration. When your opponent receives priority to cast instants or activate abilities, the Bears are already tapped — they cannot be tapped again by something like Icy Manipulator to remove them from combat, because they're already tapped.

If instead you attacked with an Angelic Wall that had been granted vigilance, it would remain untapped through the entire combat and beyond, able to block on your opponent's next turn.