Let's assume that one has some HP printer and/or scanner and checked its support status on the corresponding page of HPLIP site - HP Developer Portal | All Supported Printer Models.
So one have the following information: the device Model name, Min. HPLIP Version and Driver Plug-in need.
What should one install to make Ubuntu fully support the HP printer and/or scanner?
Currently Ubuntu have the following HPLIP versions in universe pocket:
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:
(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: