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Similar to how Layer 1 networks have different approaches to consensus, each layer 2 network will implement a scaling solution, or means to map transactions back to its layer 1. For instance, a commonly discussed layer 2 scaling solution is the implementation of zero-knowledge rollups. The idea is that a side-chain performs transaction ordering and processing and submits mathematical proof that they have processed the transactions fairly. Some examples of layer two scaling solutions are the Lightning Network, Polygon, and Starknet. The majority of scaling layer two solutions depend on cryptographic systems. For resources on the cryptography behind zero knowledge proofs I recommend this resource. The watered down version of what is happening, is that a mathematical proof is created by a verifier that some knowledge is correct.
Bitcoin - Consensus: Proof of work, Native Token: BTC Ethereum - Consensus: Proof of work (moving to proof of stake in Eth2), Native Token: Eth Algorand - Consensus: Proof of Stake, Native Token: Alg Hedera - Consensus: Proof of Stake, Native Token: hbar Cardano - Consensus: Proof of Stake, Native Token: Ada