Mars is the fourth planet in the Solar System and mentioned frequently throughout Gundam. Until Gundam AGE, the planet doesn't play an important role in any Gundam animation aside from manga series that use Mars or people from it for several storylines or events.
The red planet is mentioned in the manga Gundam F90, where it is revealed that the planet became home to some refugees from the Principality of Zeon after its defeat in the One Year War. These refugees, known as Mars Zeon, settled at the volcanic mountain Olympus Mons, where they established a base to repair their ships and Mobile Suits. In UC 111 it became known, that these Mars Zeon (also called Oldsmobile Army due to their use of outdated mobile suits) had converted Olympus Mons into a giant cannon which they planned to use to attack Earth. As a result the so-called Mars Autonomous Squadron was sent there to defeat the Mars Zeon, a task which they were able to complete.
A few decades later, Mars becomes the stage for the events of New Mobile Report Gundam Wing: Frozen Teardrop, where the planet has become a thriving society in its own right, thanks to an algae which sped up the terraformation process. However, with the growth of Mars as a society, political trouble brews, and a new war is on the verge of breaking out between Mars' Lanigreen Republic and the ESUN.
In the Cosmic Era timeline, Mars became a safe haven for both Naturals and Coordinators, who decided to escape the conflict at the Earth Sphere. Over time several colonies were established around Mars, among them the Australis colony, where its inhabitants were genetically altered to fulfill certain roles in society. Mars plays the biggest role in the manga series Gundam SEED C.E. 73 Δ Astray, which stars the crew of the Mars ship Acidalium who traveled to the Earth Sphere. There its crew members Ergnes Brahe and Nahe Herschel meet up with representatives of the various governments and try to get information about the situation and possible threats to Mars. In this series it is revealed, that Mars has trading relationships with Earth but keeps it a secret, that on Mars a rare metal exists which is important for the production of Neutron Jammer Cancellers.
In the Advanced Generation timeline, humanity migrated into space enacted under the Earth Federation's Mars Colonization Plan (also known as "Mars Birthday") 35 years' prior to the adaption to the A.G. Calendar. 150 years before the beginning of the series, people moved to the sixteen experimental colonies that were constructed in the Mars sphere. While Mars was initially thought to be a resource-rich frontier with sufficient space to address humanity's overpopulation, the colonization project failed when a botched terra-forming produced harmful particles from the surface which eventually lead to the fatal disease known as "Mars rays". The disease killed 20% of the settlers, and was named as such as the harmful particles can interact with the plasma in solar wind and produce aurora-like effects. The settlers were unable to prevent the spread of disease. With the botched investigations that followed, the migration plan was deemed a failure by the Federation government and was subsequently covered-up with the official report stating that there were no survivors.
The struggling population that remained in the Mars sphere founded a new nation led by Fezarl Ezelcant, with the desire to return to the Earth sphere. The new nation was called Vagan, and would be recognized as the Unknown Enemy by Federation forces. In hopes of finding a safe refuge on Earth, they instigated the One Hundred Years War by attacking the space Colony Angel in A.G. 101. By A.G. 201, several years after the end of the war at the Battle of La Gramis, Vagan and Earth Federation scientists were able to use data from EXA-DB and the AGE System to create the Everse System; thereby nullifying the Mars Rays and making Mars a safe refuge for the Vagan.
The Martian city of Chryse wants independence from the Earth Sphere.