Continuous monitoring of vital signs is of paramount importance. These critical physiological parameters play a crucial role in the early detection of conditions that affect the well-being of a patient. However, conventional contact-based devices are inappropriate for long-term monitoring. Besides mobility restrictions, they can cause epidermal damage, and even lead to pressure necrosis. In this paper we present a selection of recent works towards enabling the contactless monitoring of vital signs using radar devices. The selected contributions are threefold: an algorithm for recovering the chest wall movements from radar signals; a random body movement and interference mitigation technique; and a robust and accurate adaptive estimation framework. These contributions were tested in different scenarios, spanning ideal simulation settings, real data collected while imitating common working conditions in an office environment, and a complete validation with premature babies in a critical care environment.