Proof of burn
Proof of burn is a potential alternative to proof of work and proof of stake as a "scarce resource" to be exhibited by miners competing for the stream of rewards (minted coins and transaction fees) which a cryptocurrency's design makes available. The idea is that miners should show proof that they burned some coins - that is, sent them to a verifiably unspendable address. This is expensive from their individual point of view, just like proof of work; but unlike proof of work, it consumes no real resources from a whole economy perspective. This has interesting implications, discussed below.
There are likely many possible variants of proof of burn. This page currently describes Iain Stewart's version. Other people can add variant versions that still belong to the broad proof of burn idea.