Ethereum was launched in 2015 and supports 10-15 tps (transactions per second). This is obviously not enough for a protocol that aims to be the backbone of a global decentralized financial system or even the "world computer".
Ever since it was clear, that Ethereum must evolve to continue to be usable. Otherwise, high transaction costs (in the form of gas fees) will deter users from using it.
Ethereum 2.0 is a set of protocol upgrades that improve the scalability of Ethereum itself (layer 1). This can be achieved by switching the consensus mechanism from Proof-of-Work to a Proof-of-Stake algorithm (an event called "the merge" - expected end of 2021/early 2022). The beacon chain, which represents the new consensus layer is already live since Dec. 2020. Also, "Sharding" will improve the storage of data (64 shards instead of 1 chain). This will be implemented at a later stage.
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As the creator of Ethereum himself, Vitalik Buterin, notes - the future of Ethereum is based on rollup technology - also known as "layer 2". read more here
Rollup technology broadly can be separated into optimistic rollups and zk-rollups. Examples for the former are Optimism and Arbitrum, while an example for the latter is zkSync. Other scaling solutions include the plasma-based commit chain Polygon (formerly Matic) and the custodial sidechain procotol SKALE.
A testnet is technically the same code as a production network. The difference is that it is usually free to obtain native tokens such as ETH and thus ideally suited for testing.
Well-known Ethereum testnet include: