There is not much known of the Grebulons' appearance, except that they are all slightly "thin" and "discoloured". None of them have any names, as they cannot think of any, except from their leader who is simply named Leader. Leader is said to look "much like the others" except "probably a little less thin" and looking like "some guy in costume and make-up".

The Grebulons travelled across the galaxy in a sub-light spaceship and as such were in stasis during their trip. For millennia, the ship was "deeply dark and dormant", and these dormant passengers had their minds and memories stored within the ship's computers. Their main computer was the victim of a passing meteorite and while they survived in stasis, these memories, most of their central mission module, and the part of the ship that should have been able to detect that it had been struck by a meteorite were destroyed. The only information that it was able to reconstruct of their mission was "...Land...," "...safe distance..." and "...monitor it, and..."

With no other options, they decided to land on the first planet they found and monitor the first thing of interest that they detected. The Grebulons landed their ship on the planet Rupert, the tenth planet in the Sol Star System, and they began to monitor all transmissions from the only planet with life in the system: Earth.

The Grebulons became infatuated with Earth; eating McDonald's hamburgers, watching television, and furnishing their ship with human inventions such as waterbeds and hi-fi audio systems. In order to collect these items, they had a special box number in New Hampshire where they made regular pickups, and paid via American Express. They also became enamoured with astrology and invited the alternate Earth's Tricia McMillan to Rupert to map out their astrological horoscopes and offered her reheated chicken nuggets.

In a misguided attempt, the Grebulon Leader ordered Earth destroyed before it could rise into Capricorn. As a classic Taurus, this was very ominous for him. He ended up having a bad month indeed as there were no longer transmissions from Earth to monitor.

While trying to save Random from the Earth's destruction, Trillian revealed that the Grebulons are a missing reconnaissance fleet from the war that she was meant to cover; but never happened, due to the Grebulons and their army never arriving.

The meteorite that struck their ship was influenced by the Guide Mark II via Reverse Temporal Engineering as instructed by the Vogons.