Various medical systems exist for monitoring people in daily life, but they typically require the patient to wear a device, which can create discomfort and can limit long-term use. Contactless vital-sign monitoring would be preferable, but such technology is challenging to develop as it involves weak signals that need to be accurately detected within a practical distance, while being reliably distinguished from unwanted disturbance. Here, we show that a radar-based sensor can be used to monitor the individual vital signs (heartbeat and respiration) of multiple people in a real-world setting. The contactless approach, which does not require any body parts to be worn, uses two antennas (one transmitter and one receiver) and algorithms for target tracking and rejection of random body movements. As a result, it is robust against moderate random body movements (limb movements and desk work) and can keep track of individual people during vigorous movement (such as walking and standing up).