How to install HPLIP on my Ubuntu to support my HP printer and/or scanner?

Currently Ubuntu have the following HPLIP versions in universe pocket:

bionic (18.04LTS): 3.17.10+repack0-5
focal (20.04LTS): 3.20.3+dfsg0-2
hirsute (21.04): 3.21.2+dfsg1-2
impish (21.10): 3.21.6+dfsg0-0ubuntu1

This leads to the following variants.

HPLIP installation

(a) Required HPLIP version ≤ repository HPLIP version

So if one sees that Min. HPLIP Version is lower or equal to the version of the HPLIP package from repository, then the installation of the following packages will be enough with:

sudo apt-get install hplip hplip-gui

(b) Required HPLIP version > repository HPLIP version

If one sees that Min. HPLIP Version is greater than the version of the HPLIP package from repository, then one needs to install binary HPLIP by following my other answer.

(o) Optional HPLIP binary/proprietary plugin/driver

If one sees that Driver Plug-in is set to yes (or required), then one needs to install the binary/proprietary plugin/driver by following my other answer.

Examples for Ubuntu 18.04 LTS (hplip 3.17.10) and some HP device models: