Respiratory rate is a fundamental vital sign that is sensitive to different pathological conditions (e.g., adverse cardiac events, pneumonia, and clinical deterioration) and stressors, including emotional stress, cognitive load, heat, cold, physical effort, and exercise-induced fatigue. The sensitivity of respiratory rate to these conditions is superior compared to that of most of the other vital signs, and the abundance of suitable technological solutions measuring respiratory rate has important implications for healthcare, occupational settings, and sport. However, respiratory rate is still too often not routinely monitored in these fields of use. This review presents a multidisciplinary approach to respiratory monitoring, with the aim to improve the development and efficacy of respiratory monitoring services. We have identified thirteen monitoring goals where the use of the respiratory rate is invaluable, and for each of them we have described suitable sensors and techniques to monitor respiratory rate in specific measurement scenarios. We have also provided a physiological rationale corroborating the importance of respiratory rate monitoring and an original multidisciplinary framework for the development of respiratory monitoring services. This review is expected to advance the field of respiratory monitoring and favor synergies between different disciplines to accomplish this goal.