The First Robotech War is the name of the epic clash between humanity and the alien race known as the Zentraedi. It began with the preemptive strike by the SDF-1 when the ship detected the presence of the aliens and fired its main gun. As the Zentraedi swarmed the Earth, trying to capture the ship, Captain Henry Gloval managed a Space Fold that took the ship to Pluto. The majority of the First Robotech War is the ongoing battles waged against the ship as they journeyed back to Earth.
Once they reached Earth, however, the war was definitely brought home. The Zentraedi, no longer interested in capturing the ship but destroying humanity, launched a genocidal weapon called the Rain of Death which exterminated most of the population. However, the survivors of the attack did manage to retaliate, eventually getting several of the aliens to successfully negotiate peace.
The war was thought to be over after the peace talks, but the insane Commander Khyron launched a surprise suicide attack, destroying the SDF-1, and killing Henry Gloval. With the death of Khyron, however, the war was truly over.