They are the Wattersons' stuck-up next door neighbors. They are grey puppet creatures who hate their neighbors with a passion. Gaylord Robinson is almost always grouchy and deeply despises Gumball for annoying him all the time, only that Gumball idolizes him for whatever reason. Margaret Robinson is just as grouchy as her husband and always in a bad mood. She never speaks; the only vocalizations she can make are hoarse whispers. They are the parents of Rocky Robinson, and do not seem to have a good relationship.
In the episode The Poltergeist, Gumball finds Mr. Robinson and puts him in the attic, discovering that his wife left him after he lost his grouchiness and stopped arguing with her. Gumball and Darwin make several failed attempts to make Mr. Robinson grumpy again, but soon get him so angry that he tries to destroy their yard, but manage to rebuild his relationship with his wife. This episode proves that the two show their love for each other by constant bickering.
In The Car, the Robinsons make Gumball and Darwin do several chores around their house. Gumball and Darwin complete the chores immediately, much to Mr. Robinson's dismay. However, the kids accidentally destroy his car and decide to hide. The Robinsons soon find out about this, and they intentionally destroy the Wattersons' car as payback, getting themselves arrested in the process for vandalism and assault.
It is shown in The Wicked that Margaret Robinson enjoys deliberately causing pain and misery to others. Gumball and Darwin's attempts to change her prove futile, to the point where she refuses to help and even smiles evilly at a choking Darwin. Her acts included feeding squirrels coffee beans (which in turn drove them to attack civillians) and driving the Wattersons' car through the mall, framing Gumball and Darwin both times. Karma thankfully catches up to her at the end of the episode.