To kill or remove an Indestructible
Indestructible means the permanent cannot be destroyed. Something would be destroyed if something says to destroy it, or if it takes lethal damage (e.g. a 3/3 takes 3 damage, or is dealt damage by something with deathtouch).

Terror and Wrath of God don't do anything to it. An indestructible creature isn't regenerating from destruction, it just isn't destroyed in the first place.

The common ways we remove an indestructible permanent are:


Put it into any other zone:


Exile it. This means Swords to Plowshares works.
Return it to its owner's hand (known as "bouncing" it): Drag Under, Peel from Reality, and others.
Put it back into its owner's library (known as "tucking" it): Condemn, Chronostutter, and others.

Make its controller sacrifice it.
If it's a creature, reduce its toughness below 0, such as with Tragic Slip.


There are some oddball other methods, such as making it a non-issue (Song of the Dryads) or unable to participate meaningfully (Claustrophobia, Arrest), or making it lose its abilities (Snakeform, Gift of Tusks), or just lose indestructible specifically.