Respiratory rate (RR) is an important physiological parameter whose abnormality has been regarded as an important indicator of serious illness. In order to make RR monitoring simple to perform, reliable and accurate, many different methods have been proposed for such automatic monitoring. According to the theory of respiratory rate extraction, methods are categorized into three modalities: extracting RR from other physiological signals, RR measurement based on respiratory movements, and RR measurement based on airflow. The merits and limitations of each method are highlighted and discussed. In addition, current works are summarized to suggest key directions for the development of future RR monitoring methodologies.