A simple list of installed packages
max@wonko:~$ aptitude search '~i' -F '%p'
Search for installed packages from the testing repo
max@wonko:~$ aptitude versions '~i ~Atesting' --group-by=none
Finding why a package is installed
I found fonts-font-awesome
in my headless server, but there’s a reason
max@wonko:~$ aptitude why fonts-font-awesome
i owncloud Depends fonts-font-awesome
Select packages that were removed but not purged
max@wonko:~$ aptitude search '~c'
Search in the package description
max@wonko:~$ aptitude search '~d"web browser"'
Upgradable packages
max@wonko:~$ aptitude search '~U'