The hereditary ability of the Kuruneko family to pick up stray cats is the central force of this story. The author, known as Kuruneko Yamato or Mr. Kuru, finds herself continuing a family tradition where her father once brought home puppies and her mother could not resist a roadside kitten. This compulsion leads to a home filled with felines, forming the basis for a manga that blends daily life and drama.

Happy Happy Kuruneko serves as a direct continuation of the earlier series Kuruneko, following the lives of the artist and what is known as the second generation of her cats. The setting is primarily the artist's home in Japan, where she lives with her husband and a constantly evolving group of rescued cats. The narrative focuses on the small, heartwarming, and often humorous episodes that arise from cohabiting with animals, each with distinct and sometimes difficult personalities.

The manga covers several notable narrative arcs, most prominently the passing of the first generation of cats, including beloved characters like Miwa Yume, Poco, Karasubon, and Tomekichi. Their deaths from old age and illness mark a significant emotional transition in the story. The series then shifts focus to the second generation, which includes cats with special needs, such as Kotetsu, who was rescued from a highway with a fractured leg, and Momosuke John Malkovich and Koyuki Joe Apollovic, two brothers with cerebellar movement disorders. Other members like Tom, a timid Russian Blue, and Coma, a cat rescued from a hoarding situation, join the household, each with their own stories of rescue and adjustment. The narrative continues to explore the daily chaos and tenderness of life with many cats, including caring for new rescues, dealing with mischievous behavior, and the deep bonds formed through these shared experiences.