The study of human–animal interactions has become a prominent research field. The presence of pets in our daily lives has meant a change in the perception of our relationship with pets. One of the new lines of research that has opened up in this area analyzes the possible physical, emotional, and psychological benefits of a human–animal bond. In this context, two main objectives were pursued in this study, whose sample (N = 1436) was investigated in Puerto Rico: (PO1) determining the characteristics of the owners and the care of the pets within Puerto Rican society and (PO2) to analyzing the benefits of living with pets for health and personal well-being, especially at the psychological level. We sought to identify the feelings that arose in pet caretakers as a result of human–animal interactions. The methodology used, which was descriptive and not experimental, was based on a questionnaire of 86 questions with a Likert scale. After the descriptive analysis was undertaken through a frequency analysis, a binary logistic regression was carried out to establish whether the feelings and emotions of the subjects toward their companion pets were determined by sociodemographic variables and were related to the type of coexistence with their pets. The two main results from this study are as follows: for most owners, their pets are very important beings, and those who establish an emotional connection with their pets experience love, joy, and peace. Pets are part of human life through very intense relationships and interactions that, in most cases, increase personal welfare by providing improvements to the human–animal biopsychosocial system. In this sense, a relationship with a pet has a positive impact on the mental health of the owner. Pets are a part of our family lives and are regulators of the most elementary feelings and emotions in humans.