How do L2s work?

Could you elaborate on the workings of Layer 2 solutions in the cryptocurrency space? How do they help alleviate some of the scalability and transaction speed issues that are often associated with Layer 1 blockchains? Additionally, what are the main benefits and drawbacks of implementing Layer 2 solutions, and how do they compare to alternative scaling methods? I'm particularly interested in understanding the technical mechanisms behind these solutions and how they interact with the underlying Layer 1 blockchain.