A variety of physical, emotional, and mental factors can induce a stress response in pet dogs and cats. During this process, hypothalamus–pituitary–adrenal (HPA) and sympathetic–adrenal medulla (SAM) axes are activated to produce a series of adaptive short-term reactions to the aversive situations. Meanwhile, oxidative stress is induced where there is an imbalance between the production and scavenging of reactive oxygen species (ROS). Oxidative damage is also incorporated in sustained stress response causing a series of chronic problems, such as cardiovascular and gastrointestinal diseases, immune dysfunction, and development of abnormal behaviors. In this review, the effects and mechanisms of dietary regulation strategies (e.g., antioxidants, anxiolytic agents, and probiotics) on relieving stress in pet dogs and cats are summarized and discussed. We aim to shed light on future studies in the field of pet food and nutrition.