I have macOS Sierra v10.12.5 - apple support says it is out-of-date. What is the latest version?

Big Sur is the current OS, but that doesn't mean your computer can run it. We can provide more specific advice if we know more about your computer model, year, and specifications. To get more information about your computer choose Apple menu  > 'About This Mac' in the upper left corner of any window, then "More Info..." or "System Report". Copy and paste the information here, but omit the serial number and UUIDs (if present). More about this in "About System Information [Profiler] on your Mac" - https://support.apple.com/HT203001

You can also use the computer information and the links below to yourself determine what is possible with your computer.

Click on this link to read how to get different versions of macOS - https://support.apple.com/HT211683

- This article also has links to system requirements for each OS version which you should check against your exact computer model. Note some of the model identifier articles are outdated. For any model produced in the last 5 years or so you should use the system requirements links for each OS version instead. This web site also has a reliable presentation of model and OS version compatibility: https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

- Make sure you have more RAM than what is noted as "minimum" for any particular system or your computer may run slowly.

- You may find you need to use Safari to get links for High Sierra and later using the Mac App Store application to open a functioning page.

- Sierra, El Capitan, and Yosemite download as a .pkg. Click on this to have a converted version placed in your Applications folder as an "Install OS..." application. Run the installer and follow the directions.

- Upgrades may take some time (up to an hour or more) to install, with restarts and blank screens.

Back up your data in case something goes wrong --> Back up your Mac with Time Machine - https://support.apple.com/HT201250 or use a cloning tool.

Check if your old apps will still work with with the OS you want to install - https://roaringapps.com/apps This is particularly critical if you are upgrading to Catalina or newer.

I have a similar problem, trying to update from 10.12.6. My MacBook Air is capable of being upgraded to 10.13 but the link posted in this thread to the Apple support for older versions takes me to iTunes to find the dmg for 10.13, and iTunes says the file isn't available in the Store. So how do I find it some other way?

Read the link to old OS versions and follow the one to the OS you want. Open it in Safari. It should not be opened iTunes, it should open the Mac App Store App.

By the way, since your question is not identical to the one made by the original poster it really should be put in its own topic otherwise it can start to get confusing when we are helping two people in one topic. :-)

Sorry for confusing the thread. Thanks for the advice about using Safari to open the link to the OS download - I was using Firefox which meant it didn't work!