Here's a quick explainer video, or scroll down for more info
The Lightning Network went from concept in 2013/14 to active network in 2017. In true Bitcoin style, the network launched before the developers officially launched it themselves. BitRefill set themselves up a node and offered to open channels and sell gift cards in a bold and daring move.
The Bitcoin community pounced on the opportunity and the Lightning Network grew, rapidly, as nodes were installed and channels opened between network participants.
Still under active development, with a number of interoperable implementions, the network has continued to grow and expand and a new class of apps have now been built on top of it, taking advantage of the near instant low fee transactions the network rules allow.
The Lightning Network is a peer to peer network of bitcoin nodes with ongoing agreements over the custody of bitcoin held in multisig wallets.
For your PC or Laptop
This is the blockstream implementation of the Lightning Network protocol
Electrum created and launched a Python based Lightning client in 2020, integrated with their wallet software.
LND is the name of an implementation developed by Lightning Labs, designed to facilitate on-top application development.
Mobile wallets are great for Lightning, but do come with a trade off - they're less secure.
Breez have created an incredibly useful Lightning wallet with apps built in which make Bitcoin instantly and immediately useful, straight from your mobile.
Wallet of Satoshi is quite literally one of the simplest ways to get started using Lightning. However...it is CUSTODIAL. Be aware of the implications of this.
Eclair by Acinq,(also available for desktop) is a solid implementation and one of the best mobile lightning wallets, though better suited to more advanced users.