Litecoin and Dogecoin were once the #2 and #3 cryptocurrencies by market cap, respectively.
In early 2014, when Dogecoin had just been released, the meme fever pumped the cryptocurrency to hundreds of millions of U$ valuation almost overnight.
The Scrypt key derivation function is used in both these cryptocurrencies. The goal was to make it harder to develop ASIC miners for these, allowing home users to mine these cryptos.
Bitcoin had become impossible for end users to mine after the development of ASIC-based machines which were thousands of times faster than Bitcoin Core nodes running on home PC's.
Several cryptocurrencies were then developed to try and overcome this new difficulty.
Sharing the same cryptographic function made another very cool system possible: the merged mining of Dogecoin and Litecoin. This system uses the AuxPoW technique to try and solve LTC and DOGE blocks together in one go. This way, miners don't throw away all those incorrect guesses: what's wrong for a Litecoin block could be the solution to a Dogecoin block and vice-versa.
The combined mining has saved Dogecoin over the last couple of years. Doge faced some technical issues, a major scam and other hard hits, but it still survived and still clings on to the top 100 cryptos with a market cap of over U$ 600 million dollars.
Litecoin, on the other hand, has gained lots of recent popularity and is back among the top 5 cryptos with a $11+ billion dollar market cap! Its very low fees and extremely fast transactions have made it a favorite among investors.
Both these cryptos derived from Bitcoin's source code sometime in 2013 and 2014. They've adapted well over the years, but the Dogecoin source code tree has been stale for a while now.
Hopefully future developments will keep both these crypto pioneers in the market for a very long time ahead.