Robotech was created by Harmony Gold in the 1980s from three unrelated anime. The reason for this was that each of the three shows, while having all kinds of merchandise Harmony Gold wanted to sell, was too short on its own to be syndicated on American television. The three shows were edited together with small changes to character relations and terminology.
The Macross Saga
The most popular of the three parts of Robotech, it is based on Macross. This saga introduced the transforming Veritech jets, the Super Dimension Fortress, and the Zentraedi. It follows the crew of the SDF-1 and the Robotech Defense Force as they accidentally teleport to the edge of the solar system during an alien attack, travel back to Earth, and then try unsuccessfully to stop the alien Zentraedi from bombarding all of Earth. The series ends with the effort to rebuild the destroyed Earth by both humans and defecting Zentraedi, and with the main characters traveling into space on the SDF-3 after the SDF-1 and uncompleted SDF-2 were destroyed in the final battle with Zentraedi loyalists.
Robotech: Battlecry takes place during this storyline.
The Southern Cross Saga
The second storyline of Robotech was based on Southern Cross. Southern Cross' alien planet was changed to the post-apocalyptic Earth, and the series protagonist was changed into the future version of Max and Myria's daughter, despite the fact that the two girls had different hair colors. This is the least popular of the three series, the one that fit the least with the rewrites, and the one that has not had its mech designs reused for any later series.
The Invid Invasion
The final part of the original Robotech saga was based on MOSPEADA. It introduced the alien Invid, and the Cyclone transforming motorcycle armors. It takes place on an Earth that has finally ecologically recovered from the Zentraedi bombardment, only to be invaded by the "Robotech Masters", who had originally built the SDF-1 and were looking to reclaim its technology.
Robotech: Invasion takes place during this storyline.
Harmony Gold still owns the licenses for all three shows in the United States, and has worked on original works based on their Robotech storyline. The first was the original cartoon Robotech II: The Sentinels, but that ended prematurely after it ran out of funding. Its storyline was later finished in a series of novels. More recently the movie Robotech: The Shadow Chronicles came out, which continued the storyline of the original Robotech series.
Harmony Gold's death grip on the Macross franchise is often cited as why it is so difficult for Macross merchandise, anime, and video games to be released outside of Japan. They are also rumored as being the main reason why talks to release Super Robot Wars Alpha in English fell through.