Many posts around say that you shouldn't manually update Joomla 3.5+. And there are various reasons that this is good advice.
However, you can manually update Joomla 3.5+ to the latest version (currently 3.8.8).
1. Backup first
First, you need to have a good, working backup of your current site. Things may go wrong.
2. Login to administrator
It's important to have an active session in the site's administrator, while it is still working, or step 4 may not work.
3. Extract the files
You can download the latest Joomla upgrade package, either from your Joomla Update component (
Components > Joomla Update), or from downloads.joomla.org.
libraries directory to
Place the package you downloaded in the root directory of your site. Extract.
If you open your front-end, and get an error, or a blank page, you can try to rename the
libraries directory again, to
libraries-broken and copy a
libraries directory directly from the latest version full package.
4. Fix Database
If you have done well so far, your administrator should be broken. If not, hurray! Go to
Extensions > Manage > Database and click the
If your administrator is broken, copy the following link after your site's administrator URL:
If you click that link, the database should be automatically fixed, and your administrator will be usable again. Click
Fix one more time.
Your site should now have the latest Joomla version.
If you still have problems with it, you may need to update third-party extensions, or similar.