When this creature enters, it explores. (Reveal the top card of your library. Put that card into your hand if it's a land. Otherwise, put a +1/+1 counter on this creature, then put the card back or put it into your graveyard.)
Not legal in Alchemy, Premodern, Pre-EDH, Old School
Notes & Rules Information
If an ability instructs a creature to explore, its controller reveals the top card of their library. If it's a land card, they'll put it into their hand. Otherwise, they'll put a +1/+1 counter on that creature, then choose to either leave that card on top of their library or put it into their graveyard.
(2023-11-10)
If no card is revealed, most likely because that player's library is empty, the exploring creature receives a +1/+1 counter.
(2023-11-10)
If a resolving spell or ability instructs a specific creature to explore but that creature has left the battlefield, the creature still explores. If you reveal a nonland card this way, you won't put a +1/+1 counter on anything, but you may put the revealed card into your graveyard. Effects that trigger "whenever a creature explores" trigger as appropriate.
(2023-11-10)
Some spells or abilities might cause a creature to explore multiple times in a row. If you reveal a nonland card when a creature explores and leave it on top of your library, then the creature explores again immediately afterwards, you'll reveal the same card again.
(2023-11-10)
Once an ability that causes a creature to explore begins to resolve, no player may take any other actions until it's done. Notably, opponents can't try to remove the exploring creature after you reveal a nonland card but before it receives a counter.
(2023-11-10)
In some unusual cases, noncreature permanents may explore. For example, if the creature card returned by Defossilize is somehow not a creature once it's on the battlefield, it can still explore. You'll take all the same actions, and you may end up putting a +1/+1 counter on the permanent. (Note that some effects target a creature, and those effects would still require a legal target to have it explore.)
