We've all been there.
After a long game, you've got your friend on the ropes. You killed all his Elves with blocks and combat tricks, and your copy of Kalitas, Traitor of Ghet is a 7/8. Next turn you can swing for the win.
Then he taps out for Impervious Greatwurm.
Okay, that's a problem. Good thing you have another copy of Doom Blade ready to go. You tap two mana, target the Greatwurm, and… your friend is smirking. He points back at the Wurm.
If a creature has the keyword "indestructible," it means two things:
That means our little friend Darksteel Myr…
...can't be Murder, Impale, or Drag to the Underworld. It's also impervious to Lightning Bolt, Fireball, and Shivan Meteor.
You could cast Star of Extinction and that little Myr would just crawl out of the smoldering crater and wonder where everybody went.
Indestructible creatures also ignore deathtouch. Normally, a creature is destroyed if it takes damage from a creature with deathtouch. But since indestructible creatures can't be destroyed, they're immune. Darksteel Myr could block Ambush Viper until the end of time without suffering any ill effects.
So if your opponent casts Darksteel Juggernaut, what are you supposed to do? Chump block until you inevitably lose?
Thankfully, no. Just because you can't "destroy" an indestructible creature doesn't mean you can't get it off the battlefield.
If you can't face your problems, send them somewhere else. Creatures in exile are as good as dead. Better, in fact, because while there are plenty of ways to bring a creature back from the graveyard, there are hardly any to bring them back from exile.
White and black have plenty of ways to banish creatures to the shadow realm.
This is sort of a rules hack. When a creature has 0 or less toughness, it's put into its owner's graveyard as a state-based action. Since this rule specifically says "put into its owner's graveyard" and not "destroyed," this also applies to indestructible creatures.
Black has tons of ways to reduce a creature's toughness.
Okay, you can't destroy Darksteel Myr. But what if your opponent just… puts it in their graveyard? All on their own?
There are plenty of black cards that force your opponent to sacrifice a creature, dumping them out of play like expired sushi. Most of these cards don't let you choose which creature your opponent sacrifices, but if there's only one option (say, because you killed everything else), they have to ditch it.
These three solutions are generally the best way to handle indestructible creatures. They answer the problem permanently, and they work just as well against non-indestructible creatures, so they're useful no matter what you're facing.
Unfortunately, with a few exceptions, they're only available in white and black. If your deck can't play these cards, it's time to look at other options.
Pros: Countermagic can solve any problem! Well, almost any.
Cons: Useless if the indestructible creature is already on the battlefield.
Color(s): White and blue.
Pros: Works on almost any creature.
Cons: Many offensive Auras hinder a creature, but don't remove it entirely. If your opponent destroys the Aura, you're right back where you started.
Pros: Solves the problem before it starts.
Cons: Like countermagic, it doesn't help if the creature is already on the battlefield.
Color(s): White and blue.
Pros: Like a soft form of exile.
Cons: They can always draw it again.
Pros: Like duct tape, it's a cheap and easy solution.
Cons: Like duct tape, it's not a permanent solution.
Sometimes, there's just no way to get rid of an indestructible creature. Maybe you didn't draw the card you needed. Maybe your deck is red or green, and the only creature removal you have relies on damage.
When that happens, you need a plan that lets you win without getting rid of the indestructible creature.
Yes, Darksteel Myr can block Ghalta, Primal Hunger a million times. But your opponent will still take 11 damage each time. That's 11,000,000 damage, which is hopefully enough to win you the game.
"Oh no, your Darksteel Myr blocked one of my 10 2/2 Plant tokens. I guess you only take 18 damage this turn instead of 20."
Darksteel Myr can't block Shivan Dragon or defend your opponent from Lava Spike. Focus on damaging your opponent, and it won't matter if their creature lasts the whole game.
If you really need more ways to get rid of your friends' indestructible creatures, the following cards offer permanent solutions and can be cast with any color of mana.
Colorless cards that can exile creatures aren't very common. But even among the rare exceptions, Duplicant stands out by not just eliminating your opponent's creature, but giving you one of your own. If the creature you eliminate has a lot of power and toughness (like, say, Impervious Greatwurm), your opponent is going to be in a lot of trouble.
It's very rare that you'll go up against more than one indestructible creature at once. If you do, however, Shadowspear ability can make all of them destructible for just one mana. I wouldn't run this over Duplicant or another exile effect most of the time, but if one of my friends decides to build a deck full of Gods and Darksteel artifacts, I'm slotting Shadowspear no questions asked.