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The Ethereum subreddit has this post related to an Ethereum-Dogecoin sidechain.

What is a sidechain?

Could one sidechain be a private Ethereum network?

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Put simply, sidechaining is any mechanism that allows tokens from one blockchain to be securely used within a completely separate blockchain but still moved back to the original chain if necessary. By convention the original chain is normally referred to as the "main chain", while any additional blockchains which allow users to transact within them in the tokens of the main chain are referred to as "sidechains". For example, a private Ethereum-based network that had a linkage allowing ether to be securely moved from the public Ethereum main chain onto it and back would be considered to be a sidechain of the public network.

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    What are a few other examples?
    – mowliv
    Commented Oct 22, 2016 at 18:08
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    @mowliv I think a good way to think about it is by looking at our economy. The Federal Reserve prints US dollars for the US Government (the main blockchain) to boost the US economy. However, US dollars can be exported to other countries (a side chain) that could have a completely independent economy but still use a currency backed by the US government.
    – Olshansky
    Commented May 30, 2017 at 0:56
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    @Olshansk not a great example for lots of reasons. A better example would be: if a doge-ethereum linkage was built that allowed doge users to exchange their doge for a specific erc20 token on ethereum and vice versa. There is actually a bounty out there for this one.
    – Jeff Coleman
    Commented Jul 14, 2017 at 17:49
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    are people using sidechains to improve performance of an application? if i want to create my own ethereum based tokens and allow users to acquire tokens, I could create them on a sidechain with a shorter block time than mainnet, and sync token balances in a separate process, yes?
    – Luke W
    Commented Jan 29, 2018 at 21:17
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Sidechain is a blockchain that runs in parallel to the main blockchain which extends functionality through interoperable blockchain networks allowing a decentralized way of transferring/synchronizing your tokens between the two chains. In other words, you can move your cryptocurrency to the sidechain and then back to the main chain.

Sidechains are decentralized, peer-to-peer networks that provide useful enhancements (such as security, risk, and performance) for global systems of value exchange that don’t need any other third parties. They enable developers to safely develop new applications without a risk.

They're very similar to Bitcoin sidechains. They tend to improve scalability, but only indirectly by enabling innovation.

Related:

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Here is a wonderful explanation of state channels and sidechains, their working and how they differ from each other, and their pros and cons.

According to the article:

State channels are the general form of payment channels, applying the same idea to any kind of state-altering operation normally performed on a blockchain.

The basic components of a state channel are very simple: enter image description here

  • Part of the blockchain state is locked via multisignature or some sort of smart contract, so that a specific set of participants must completely agree with each other to update it.
  • Participants update the state amongst themselves by constructing and signing transactions that could be submitted to the blockchain, but instead are merely held onto for now. Each new update “trumps” previous updates.
  • Finally, participants submit the state back to the blockchain, which closes the state channel and unlocks the state again (usually in a different configuration than it started with).

A sidechain is a separate blockchain that is attached to its parent blockchain(mainchain) using a two-way peg.

In other words, you can move assets to the sidechain and then back to the parent chain. sidechain

The two-way peg enables interchangeability of assets at a predetermined rate between the parent blockchain and the sidechain. The original blockchain is usually referred to as the ‘main chain’ and all additional blockchains are referred to as ‘sidechains’. The blockchain platform Ardor refers to its sidechains as ‘childchains’.

A user on the parent chain first has to send their coins to an output address, where the coins become locked so the user is unable to spend them elsewhere. Once the transaction has been completed, a confirmation is communicated across the chains followed by a waiting period for extra security. After the waiting period, the equivalent number of coins is released on the sidechain, allowing the user to access and spend them there. The reverse happens when moving back from a sidechain to the main chain.

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  • Thank you for your really clear and straightforward explanation. Just a side-note (sorry :) if you link to an article on stackexchange you are supposed to disclose if you are the author of that article stackoverflow.com/help/promotion
    – MrTJ
    Commented Jul 6, 2018 at 15:31
  • Thanks for the heads up. I didn't know about the disclosure rule.
    – Vaibhav Saini
    Commented Jul 6, 2018 at 16:42
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    just to get this right: basicly the risks when using a sidechain break down to trusting the sidechain operator, right? E.g. if the sidechain is operatred by a malicious actor that actor could steal any wrapped tokens. This can also happen by accident or by 51% attacks on the sidechain (that might be not as decentralized as the mainchain).
    – omni
    Commented Feb 18, 2021 at 15:00

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