Spotlight Search displays "Indexing..." forever
When you say "never", how long? Indexing can take hours on a large mechanical hard drive. This is usually required after an OS update.

You can restart and rebuild the Spotlight index, which may help. Either use the Terminal command:

sudo mdutil -E /


(You'll then have to enter your admin password. If you've never done this before, you'll see a short warning about being careful.) 

Or go to System Preferences > Spotlight, and in the Privacy tab, drag the system volume to the list of exclusions. Then remove it.

Hanging Spotlight indexes may also be a sign of a failing hard drive, so it's also worth checking that your system volume is functioning correctly.