What is the relationship between the Gunbuster and Diebuster series? Gunbuster is one of my favorite series, and I remember learning of a sequel series called Diebuster, or Gunbuster 2. 

What is the relationship between the two shows? Does Diebuster's story relate to Gunbuster's in some way? Do any characters cross over both shows? Does Diebuster refer to the events of Gunbuster in any way?
Gunbuster was originally released as a six episode OVA in 1988. It's sequel, Diebuster, was also originally released as a six episode OVA 18 years later. Typically sequels are released around the time of the original so it's fresh in the minds of people. Without giving too much away the stories are somewhat but not directly connected, since Diebuster happens ~12,000 years after Gunbuster.

To take care of the time gap issue with Gunbuster, both series have been cut into two movies and presented as a double-feature. The references to each other are subtle.

For an example if you didn't watch Gunbuster: 


You wouldn't know that Nono appears in Gunbuster under a different name
The Diebuster ending only makes sense if you saw the ending of Gunbuster (takes place 12,000 years earlier)
You wouldn't understand the Solar System Defence System and why it was attacking
You wouldn't understand why the drive was removed from Dix-Neuf