A blockchain needs rules for who gets to add new blocks. Here are the main models, and what sets them apart.
In a blockchain there is no central party that decides what is correct. The participants still have to agree on which transactions are valid, and in what order they happened.
The rules for this are called a consensus mechanism. It keeps the network together, even when some participants try to cheat.
Proof of work is used by Bitcoin. Machines, called miners, compete to solve a computing task, and the winner gets to add the next block and receive a reward.
The model is very well tested and considered secure. The drawback is that it uses a lot of electricity and processes relatively few transactions.
In proof of stake, participants called validators lock up their own tokens as collateral. They are selected to create new blocks, and lose part of their stake if they break the rules.
The model uses far less energy than proof of work. Ethereum switched to proof of stake in 2022, and most newer blockchains use a variant of it.
Delegated proof of stake lets token holders elect a small number of validators. That gives high speed, but more power to fewer players.
Proof of authority uses validators with known identities and suits closed networks between banks or companies. Solana combines proof of stake with a cryptographic clock, proof of history, to process transactions faster.
No model is best at everything. The choice is about balancing security, speed, energy use and how many share control.