Respiratory monitoring is essential in sleep studies, sport training, patient monitoring, or health at work, among other applications. This paper presents a comprehensive systematic review of respiration sensing systems. After several systematic searches in scientific repositories, the 198 most relevant papers in this field were analyzed in detail. Different items were examined: sensing technique and sensor, respiration parameter, sensor location and size, general system setup, communication protocol, processing station, energy autonomy and power consumption, sensor validation, processing algorithm, performance evaluation, and analysis software. As a result, several trends and the remaining research challenges of respiration sensors were identified. Long-term evaluations and usability tests should be performed. Researchers designed custom experiments to validate the sensing systems, making it difficult to compare results. Therefore, another challenge is to have a common validation framework to fairly compare sensor performance. The implementation of energy-saving strategies, the incorporation of energy harvesting techniques, the calculation of volume parameters of breathing, or the effective integration of respiration sensors into clothing are other remaining research efforts. Addressing these and other challenges outlined in the paper is a required step to obtain a feasible, robust, affordable, and unobtrusive respiration sensing system.