Several parties compute a result from their private inputs and nobody learns anything else, even if all but one of them cheat.
The idea: When most participants might cheat, secret sharing alone isn't enough, so these protocols use oblivious transfer wherever two parties' secrets meet. In Yao's approach, one party encrypts the whole computation as a "garbled circuit", and the other evaluates it after picking up the keys for their own inputs through oblivious transfer. Your input stays hidden even if everyone else colludes.
Why it matters: Used for shared custody of keys and for analyzing private data.
On the map: Yao / GMW: OT + garbled circuits
Yao's garbled circuits (two parties) and GMW (many parties)[1, 2] let parties compute any function on private inputs while staying secure even if all but one participant are corrupted.
They need oblivious transfer, so public-key assumptions, plus symmetric cryptography. Where you meet it: threshold wallets and key management, private set intersection, sealed-bid auctions (Danish sugar-beet auction, 2008)[3], privacy-preserving analytics.
If any of these breaks, this breaks too.
If this breaks, these break with it.
Nothing on the map depends on it: it is an end point, something people use directly.