The paper offers an overview of signal processing approaches that are suitable for monitoring of persons by means of ultrawideband sensors. The "Monitoring of persons" is related to their detection, localization, and tracking and in the case of static persons, also to the monitoring of their vital signs such as the breathing frequency and the heart rate. This paper discusses basic principles in the monitoring of persons who can be moving, static, or changing the character of their movement. In the case of static persons, the paper describes signal processing methods suitable for contactless estimation of their breathing frequency and the heart rate. Monitoring of persons using UWB sensors is attractive in many application scenarios such as emergency, rescue, medical, etc. Therefore, we believe that this comprehensive survey brings a lot of interesting information to researchers and specialists working in the field of contactless monitoring of persons.