TweetDeck is an official Twitter client, running on Linux, Windows and Mac. It has a modern graphical interface.

TweetDeck does not work native on Linux, because of some proprietary licence issues with Adore AIR, it can be used only with Chrome and Firefox, by third party plugins. But some developers have created TWD, the TweetDeck Wrapper project, that has native support on Linux. Soon, it will be integrated better in the most popular desktop environment.
For now, it is still under development. It works well when signing in with an already existing TweetDeck account, but crashes when you want to create a new TD account, from the app. It is recommented to create a TweetDeck account on web.tweetdeck.com, to avoid the crashes.
The TweetDeck Wrapper does not require any installation, the user has to extract the archive, set execution permissions and run the app. This tutorial works for Ubuntu 13.10 Saucy Salamander, Ubuntu 13.04 Raring Ringtail, Ubuntu 12.10 Quantal Quetzal, Ubuntu 12.04 Precise Pangolin, Linux Mint 15 Olivia, Linux Mint 14 Nadia, Linux Mint 13 Maya, Debian Jessie, Debian Sid, Debian Wheezy, Debian Squeeze, Fedora 19, Fedora 18, Fedora 17, OpenSUSE 13.1, OpenSUSE 12.3, OpenSUSE 12.2 and many others.
Download TWD, for 32 bit systems:
$ wget -c https://passcod.name/twd/bin/twd-1.0.1-linux32.tar.gz
Download TWD, for 64 bit systems:
$ wget -c https://passcod.name/twd/bin/twd-1.0.1-linux64.tar.gz
Extract the archive, cd into the newly created folder and set the execution permissions:
$ tar -xzvf twd-1.0.1-linux*.tar.gz
$ cd twd-1.0.1-linux*
$ sudo chmod +x twd
To launch the app, just to:
$ ./twd
For an easier usage, you can create a desktop launcher for it, or at least, a terminal alias. This is my alias for TWD:
$ alias twd='nohup ~/downloads/twd &>/dev/null &'