Abstract-This paper reviews recent works in the literature on the use of systems based on Radar and RGB-Depth sensors for fall detection, and discusses outstanding research challenges and trends related to this research field. Systems to detect reliably fall events and promptly alert carers and first responders have gained significant interest in the past few years in order to address the societal issue of an increasing number of elderly people living alone, with the associated risk of them falling and the consequences in terms of health treatments, reduced well-being, and costs. The interest in radar and RGB-D sensors is related to their capability to enable contactless and non-intrusive monitoring, which is an advantage for practical deployment and users' acceptance and compliance, compared with other sensor technologies such as video-cameras, or wearables. Furthermore, the possibility of combining and fusing information from heterogeneous types of sensors is expected to improve the overall performance of practical fall detection systems. Researchers from different fields can benefit from multidisciplinary knowledge and awareness of the latest developments in radar and RGB-D sensors that this paper is discussing.