MikeJones just using Composer, you could do the following.
List all installed packages that have an update available:
composer show --outdated --direct
Update all packages to the newest minor version according to the requirements in composer.json (this can be time- and memory-intensive, the ideal solution is to run this command locally, test, then send composer.lock to the server and run composer install):
composer update
To update a package to the very last major update, I think there's no other option except using require with the package name (for example, to go from 0.4.* to 0.5.* or from 1.*.* to 2.*.*):
composer require <vendor/package>
As for graphical solutions, Bazaar and the Dashboard extensions list outdated extensions right inside Flarum.
