Is macOS High Sierra version 10.13.6 the current version? I keep getting messages saying it should be updated?

High Sierra 10.13.6 is the latest version of High Sierra, but not the latest version of macOS that you can run.

MacTracker shows three types of 2013 iMacs:

• iMac (21.5-inch, Early 2013)
• iMac (21.5-inch, Late 2013)
• iMac (27-inch, Late 2013)

All can be upgraded as far as macOS Catalina.

Catalina drops support for 32-bit applications, so if you have many of those you want to keep, you may want to stick with High Sierra, or upgrade to Mojave.

How to download macOS - Apple Support

What year model is the iMac?

see > Identify your iMac model - Apple Support

thomasfrommanalapan wrote:

2013

A 2013 iMac can be upgraded to macOS 10.15 Catalina.

see > Update macOS on Mac - Apple Support