Combat damage and Regeneration

[Chronatog]

How does regeneration work if damage does not go into the stack anymore?

For example, I control a River Boa and block my opponent's attacking Dwarven Vigilantes. If I regenerate my boa, does it still deal damage to the dwarf?

And how exactly, step-by-step regeneration works during the combat phase? When do I need to regenerate a creature? At the beginning of the damage step?

Played a draft another day and short circuited my brain when I tried to apply regeneration to the "new" rules.

[PirateKing]

701.13. Regenerate
701.13a If the effect of a resolving spell or ability regenerates a permanent, it creates a replacement effect that protects the permanent the next time it would be destroyed this turn. In this case, “Regenerate [permanent]” means “The next time [permanent] would be destroyed this turn, instead remove all damage marked on it and tap it. If it’s an attacking or blocking creature, remove it from combat.”
701.13b If the effect of a static ability regenerates a permanent, it replaces destruction with an alternate effect each time that permanent would be destroyed. In this case, “Regenerate [permanent]” means “Instead remove all damage marked on [permanent] and tap it. If it’s an attacking or blocking creature, remove it from combat.”
701.13c Neither activating an ability that creates a regeneration shield nor casting a spell that creates a regeneration shield is the same as regenerating a permanent. Effects that say that a permanent can’t be regenerated don’t preclude such abilities from being activated or such spells from being cast; rather, they cause regeneration shields to not be applied.

Tapping :g: and paying for River Boa's ability just gives it the text that next time it would be destroyed this turn, it isn't. Instead tap it, remove all damage from it, and remove it from combat. So if it would be destroyed through combat damage, it would be dealing combat damage itself, so yes it would mark 2 damage on Dwarven Vigilantes. If it was blocking a Serra Zealot however, the damage from first strike would break the regeneration shield and remove River Boa from combat, so it would not be able to deal damage back.
So pay for Regeneration whenever you want, your upkeep if you want, the effect will last the whole turn. Last available moment to regenerate from combat damage would be before combat damage.

[Chronatog]

Tapping :g: and paying for River Boa's ability just gives it the text that next time it would be destroyed this turn, it isn't. Instead tap it, remove all damage from it, and remove it from combat. So if it would be destroyed through combat damage, it would be dealing combat damage itself, so yes it would mark 2 damage on Dwarven Vigilantes. If it was blocking a Serra Zealot however, the damage from first strike would break the regeneration shield and remove River Boa from combat, so it would not be able to deal damage back.
So pay for Regeneration whenever you want, your upkeep if you want, the effect will last the whole turn. Last available moment to regenerate from combat damage would be before combat damage.

Thank you, this is helpful. I apparently misread/misinterpret this part of the rules in the part that regeneration is a replacement effect for damage related descruction.

[Technics]

Thank you, this is helpful. I apparently misread/misinterpret this part of the rules in the part that regeneration is a replacement effect for damage related descruction.

Just to note, it's not only damage related destruction, but any destruction. I assume you meant that but just want to make sure any wondering eyes in the future remember that.