How to upgrade Grav from v1.3.9. to latest build

I'm running a Grav powered site with Grav v1.3.9 and Admin v1.6.6

I would like to update this to the most recent versions. If I check for updates no new updates are available.

How can I do the update?

You will probably need to do it manually, because the distance between current versions and your versions are substantial. Backup your /user-folder, download and install the newest Grav + Admin, then drop the /user-folder back into it.