51 Percent Attack
An attack where one party controls enough block production to rewrite recent history and spend the same coins twice.
With a majority of hash rate on a proof-of-work chain, an attacker can mine a competing chain in private, deposit coins and receive something in return on the public chain, then publish the longer private chain so the deposit disappears while the goods do not. The powers this grants are narrow: the attacker can reorder, exclude, and reverse recent transactions, but cannot move coins from addresses whose keys it does not hold, cannot create coins outside the issuance rules, and cannot force nodes to accept invalid blocks. Smaller proof-of-work chains, including Ethereum Classic and Bitcoin Gold, have suffered documented attacks precisely because enough hash rate could be rented for less than the value that could be reversed. The proof-of-stake equivalent requires acquiring a large fraction of the stake and exposes the attacker to slashing, which destroys the capital used.
In practice
Exchanges have responded to attacks on smaller chains by sharply increasing the number of confirmations required before crediting deposits of those assets.
The common misunderstanding
A majority attacker cannot take coins from addresses it has no keys for; the attack reverses recent transactions rather than breaking cryptography.