Client mods
A Discord client mod (client modification) is a piece of software that aims to alter the functionality or look of Discord in some way. While this behavior is against the Discord TOS[1], it is common knowledge that Discord generally does not care about such projects nor the users who use them. Even their employees have been known to use them[2] and contribute back to the community[3][4]. The only exception would be when the Discord API is used abnormally or abused, commonly referred to as a selfbot.
While this only lists client modifications, some projects aim to recreate a Discord client entirely from the ground up. A complete and up-to-date list of all mods and custom clients to exist can be viewed at the Discord Client Encyclopedia.