Polygon is a suite of decentralized Ethereum scaling solutions that aim to provide developers with the tools necessary to build scalable, user-friendly dApps with low transaction fees and high security guarantees. Ethereum prioritizes decentralization and optimizes for inclusive validation, but is plagued with high transaction fees and low throughput as a result. The most popular Polygon projected, initially branded as Matic Network, is its PoS commit chain. However, Polygon announced their commitment to zero-knowledge cryptography in August 2021. A zk proof provides a method of verifying something without requiring the underlying information to be revealed to the prover. Polygon uses zk proofs to prove the validity of transactions that were executed on rollups to Ethereum mainnet. There are two types of zk proofs commonly used in crypto: Succinct Non-Interactive ARgument of Knowledge (SNARKs) and Scalable Transparent ARgument of Knowledge (STARKs). SNARKs have been around for longer and are more common as a result, but they require a trusted setup. STARKs, on the other hand, do not require a trusted setup but have a larger proof size that results in more gas consumption and longer proving times.
Polygon is commonly referred to as the 'Swiss Army Knife' of Ethereum scaling solutions given the wide scope of problems they are aiming to solve.