Simple Summary: The welfare of purebred dogs and cats is being undermined by fashion trends that popularize extreme shapes. Official descriptions of breeds require their distinctive characteristics to be compatible with good health. Nevertheless, extremes within breeds that compromise health, referred to as hypertypes, have become trendy. For example, when flat faces are taken to the extreme, dogs and cats may be unable to breathe normally, which affects all aspects of their lives. Individuals such as breeders, owners and veterinarians, and organizations in the whole community surrounding purebred dogs and cats must collaborate to prevent the breeding of hypertypes. Fashion-fueled breeding of hypertypes, whether or not illegal, must also be tackled because its negative effects can extend beyond what is visible to unsuspecting owners choosing their puppy or kitten. The problem is complex, and the solution involves many bodies working together. However, the message is simple: health, temperament, and well-being must be prioritized over appearance. Putting this into practice will help protect the much-valued diversity of breeds. Fashions in the appearance of purebred dogs and cats are encouraged by celebrity culture, social media, and online impulse buying. The popularity of characteristics perceived as cute, quirky, and anthropomorphic has driven increasingly exaggerated breed features appealing to aesthetics rather than health. 'Hypertypes' of some breeds have emerged that take a breed's distinctive appearance to extremes beyond the intended interpretation of breed standards. This has severe, direct and indirect health and welfare consequences. Extreme conformations are associated with chronic health conditions including brachycephalic obstructive airway disorder, ocular, dental, skin, and musculoskeletal disorders. Puppy and kitten farms and illegal traders that meet the demand for hypertypes are associated with poor husbandry that neglects the physical, behavioral, and mental health of parents and offspring. A multidimensional approach involving collaboration between breeders, geneticists, owners, veterinarians, kennel clubs, cat fanciers' associations, animal charities, the academic and research communities, commercial enterprises, and governments is needed to safeguard breeds and tackle these challenges. There are many ongoing initiatives by national kennel clubs and global partnerships to educate pet owners and support responsible pet ownership and sustainable breeding. The resounding message is that health, temperament, and well-being must be prioritized over appearance. [ABSTRACT FROM AUTHOR]