Some of the following Skyrim Special Edition mods can be found on Bethesda's site, but the links we'll post all point to our go-to, NexusMods. To be fair, there were other changes as well.
Thanks to the Script Extender, essentials like SkyUI are now available in this slightly prettier (it does have nicer shadows), and more stable (you can alt-tab as much as you like, and weigh it down with more mods) version of Skyrim. Once it's installed, go into Skyrim Special Edition's properties in Steam and set it to 'Only update this game when I launch it' and launch Skyrim with skse64_loader.exe, as otherwise every update to the creation club will break the Script Extender and you'll have to download a new version.
Skyrim Script Extender wasn't compatible with Skyrim: Special Edition at launch, but has been for a while now (it'll be labelled 'Current SE build' at that link). Looking for mods for the original version of Skyrim? We've selected over 100 of the best mods for improved visuals and optimization, new quests and locations, roleplaying and immersion, creatures and NPCs, and much more.