That’s right, Genpets are not toys or robots. They are living, breathing genetic animals.
We use a process called "Zygote Micro Injection" which is quickly becoming a favourable method to combine DNA, or to insert certain proteins from different species. Most notably it was used in 1997 to splice mice with bioluminescent jellyfish (link) and has since been used to create glowing rabbits, pigs, fish, and monkeys (link). Since then, human DNA has been injected into rabbits, chimpanzees, spider DNA into sheep, and now, Genpets have arrived!
Read National Geographic's site for more information on human animal hybrids (link).