Face ID doesn’t work if I am not wearing glasses.

Set up an alternate Face ID without your glasses. Settings>Face ID & Password>Set Up an Alternate Appearance.

I only wear glasses some of the time and I needed to do this so that I got recognized both with and without them.

Sounds like this person --> issue resolved, it turned out that a new pair of eyeglasses ( not sunglasses) , at night, were either dirty or reflected the light necessary to activate face id" - Face id glitch... - Apple Community

If you just have issues with Face ID not working properly, read this document: If Face ID isn't working on your iPhone or iPad Pro - Apple Support

Glad it helped!