Over time the human–animal bond has been changed. For instance, the role of pets has changed from work animals (protecting houses, catching mice) to animals with a social function, giving companionship. Pets can be important for the physical and mental health of their owners but may also transmit zoonotic infections. The One Health initiative is a worldwide strategy for expanding collaborations in all aspects of health care for humans, animals, and the environment. However, in One Health communications the role of particularly dogs and cats is often underestimated. Objective: Evaluation of positive and negative One Health issues of the human–companion animal relationship with a focus on zoonotic aspects of cats and dogs in industrialized countries. Method: Literature review. Results: Pets undoubtedly have a positive effect on human health, while owners are increasing aware of pet’s health and welfare. The changing attitude of humans with regard to pets and their environment can also lead to negative effects such as changes in feeding practices, extreme breeding, and behavioral problems, and anthropozoonoses. For the human, there may be a higher risk of the transmission of zoonotic infections due to trends such as sleeping with pets, allowing pets to lick the face or wounds, bite accidents, keeping exotic animals, the importation of rescue dogs, and soil contact. Conclusions: One Health issues need frequently re-evaluated as the close human–animal relationship with pet animals can totally differ compared to decennia ago. Because of the changed human–companion animal bond, recommendations regarding responsible pet-ownership, including normal hygienic practices, responsible breeding, feeding, housing, and mental and physical challenges conforming the biology of the animal are required. Education can be performed by vets and physicians as part of the One Health concept.