How can I uncompress a *.7z file?

First install the p7zip-full package:

sudo apt-get install p7zip-full

With this, Nautilus should have an option to uncompress 7-Zip Files.

I also recommend p7zip-rar so it also includes support for RAR files.

This is assuming you want to do it via GUI with Nautilus. If not, after downloading the packages above do the following:

7z x PACKAGE.7z 

that should eXtract the packages with full path.

There is also dtrx - which is immensely useful for un-archiving anything.

it stands for "Do The Right eXtraction" - and will uncompress anything without any fuss.

simply:

sudo apt-get install dtrx
dtrx archive.tar.XX

Manpage: http://manpages.ubuntu.com/manpages/trusty/en/man1/dtrx.1.html

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UPDATE for Ubuntu 20.04 :

According to their pypi page, dtrx is not currently available in the official repos. Thus, if you cannot install this via apt, then you can still use pip3:

pip3 install dtrx

If you don't already have pip3 installed, you can install it with

sudo apt install python3-pip

Run following command in the terminal:

sudo apt-get install p7zip-full p7zip-rar

Or search through the ubuntu software center as 7zip and unrar and install the packages.