A consensus protocol or algorithm is a set of rules according to which members of the blockchain network agree that the blockchain is valid. Here is the list of the most popular protocols:
Proof-of-Work (PoW) is the first and most reliable consensus protocol for public blockchains such as Bitcoin and Ethereum, but it is energy inefficient.
Proof-of-Stake (PoS) does not require complicated calculations. Instead, it encourages users to put their own tokens to perform an equivalent amount of transaction checks. It is believed that each participant will act rationally.
Delegated Proof-of-Stake (DPoS) is the algorithm within which members delegate the release of new blocks to a small and fixed number of elected members. Highly competitive but very profitable.
BFT is a characteristic of all decentralized consensus protocols, but its variations make individual algorithms faster and more resistant to faulty nodes. However, so far, it is useful only for small and private systems.
PBFT is a proven solution for corporate networks. Fast and secure, but relies on bandwidth.
DBFT extends BFT capabilities by allowing members of the BFT network to delegate validators. Very fast, but more centralized. While all BFT options are private blockchains, FBA is federated and public.