As of late 2022, Mendeley is no longer supporting their previous desktop product, Mendeley Desktop. If you already have it installed, Mendeley Desktop should still work but it will no longer be updated. Its functionality can't be guaranteed over the long term.
The new desktop software is called Mendeley Reference Manager; it's recommended that you switch over to Mendeley Reference Manager by downloading the new product. Your library will be automatically synced when you log into the new program with your existing account. Both can be installed on a computer at the same time, so you can set up the new program and be sure everything transferred well before you uninstall the old program.
This guide is based on Mendeley Desktop and will be updated in 2023. For the most up to date support, visit Mendeley's excellent official support guides: