When do you have to activate Zhonya's Hourglass to save a unit from dying in combat or from Icathian Rain damage?

Ruling: Zhonya's has a replacement effect, so you only need to make sure it's face up on the board before the unit actually dies. You can play it in response to whatever spell, ability, or trigger will kill the unit you want to save.

Sequence:

• In combat: Reveal Zhonya's with Focus before passing priority, because if both players pass focus you go directly into combat damage and lose the chance to play it
• With Icathian Rain: Wait until the reflexive triggers are finalized to the chain, then play Zhonya's in reaction to whichever specific trigger would kill the unit you want to save (you can wait through multiple triggers resolving)

Nuances:

• If you only control units at the battlefield where Zhonya's is hidden, and one of those units dies, you lose control of the battlefield and Zhonya's goes to trash
• The latest you can play Zhonya's is in reaction to whichever trigger would kill the unit at the battlefield with the Zhonya's (if that's the unit you want to save)
• Against Icathian Rain, the opponent should try to kill the unit at the battlefield with Zhonya's first, forcing you to save that one instead of units in base