The Third Robotech War was a conflict between humanity and the Invid over the control of the Earth. The Robotech Expeditionary Force launched at least three major assaults to reclaim Earth, all of which failed, but the third of which allowed a single pilot to start a rebellion on Earth, starting the heaviest fighting of the Third Robotech War.
The Invid were drawn to Earth after the end of the Second Robotech War when the spores of the Flower of Life were spread across Earth. The Army of the Southern Cross, greatly weakened by their war with the Robotech Masters were unable to prevent the fall of Earth. The Invid rule of Earth was brutal, swiftly exterminating any resistance to their dominance.
The arrival of the REF in the southern cross resulted in an attack by the Invid, who took them for allies of the Sentinels. As a result, they lost their Space Fold engines and could not return home to defend it. However, deciding they could still help in their own way, Rick Hunter allied the REF with the Sentinels, and moved to dismantle the Invid empire before heading home to retake Earth. In doing so, however, he unknowingly put humanity in greater danger when he authorized the use of the Haydonites Shadow Technology and their Neutron-S Missiles, both of which were trojan horses meant to destroy humanity and more importantly their supply of Protoculture, which the Haydonites despised.
Sometime after the Robotech War, a new Robotech War was about to begin between the Invid and the Humans. The Invid conquered the Earth within a few days and the Army of the Southern Cross was all but wiped out. The survivors of the army fled Earth and joined up at Space Station Liberty to await the arrival of the SDF-3 and the returning Expedition.
Earth remained occupied by the Invid for a decade, during which time they set up large scale hives and genesis pits to harvest Protoculture.
In the year 2042, the 21st Mars Division arrived at Earth as part of the second attempt to retake Earth. The fleet was intercepted before its troops could begin their atmospheric insertion, and was quickly destroyed by the Invid. Lancer Belmont and Jonathan Wolfe were part of the force and were both left stranded on Earth. (Love Live Alive)
The last of the Mars Divisions, commanded by Scott Bernard, hit Earth shortly afterwards. They were able to withstand the first Invid attack, however, the Second Invid attack destroyed them when they attempted to enter the Earth's atmosphere. Apparently only Scott survived the attack.
Scott's survival brought about a new wave of troubles for the Invid. Setting off to destroy Reflex Point or die trying, Scott began to foster a new wave of resistance against the Invid. Joined by Rand, Rook Bartley, Annie "Mint" Labelle, Jim "Lunk" Austin, and Lancer Belmont, he formed the Robotech Rebels who sole mission during the war was to destroy Reflex Point. Coordinating with other rebel cells and the remnants of Earth's previous armies, they launched a guerrilla war against the Invid as they moved closer and closer to Reflex Point. At the same time, the REF began to arrive back in their home territory, ready to launch a bold new offensive to take back Earth.
During this time, the Invid began experiments to determine whether the human form was more viable then their current form, and found that it was the form most suited to their purposes. In doing so, they created Dusty Airs, a gunslinger who was abandoned by his squadron and would dedicate his life to revenge.
Upon discovering this knowledge, they began to transform their population into humanoid warriors, but in doing so some of them began to succumb to the same problems that the Zentraedi and Robotech Masters had faced before them. While not nearly as widespread a problem due to the nature of their species, two individuals in particular paved the way: Ariel and Sera. Ariel was the princess of the Invid who had been transformed into a humanoid to spy on the Rebels, only to develop amnesia and aid them, coming to admire humanity in the process. Sera on the other hand was one of the top lieutenants to the Regess. She fell in love with Lancer and aided the rebels during the final battle.
All forces of the Rebels and REF converged during the Battle of Reflex Point, where the war was brought to an end when the Regess officially decided to withdraw rather then endure prolong the war with the REF over Earth, specially after she discovered that they were using Haydonite technology. Deciding they were too much like the Robotech Masters for their own good, she took all of humanity's supply of Protoculture as she left with the rest of the race except Ariel and Sera.
The Regis, Queen Mother of the Invid, left Earth with the rest of the Invid, taking all of the Planet's Protoculture with her.
As the Third Robotech War ended, a new Robotech War began when the Haydonites, now revealed to be the Children of the Shadow who annihilated the Invid's first homeworld, betrayed humanity and launched an all-out assault on the REF.