This article presents radar signal processing for sensing in the context of assisted living. This is covered through 3 example applications: human activity recognition for activities of daily living, respiratory disorder and Sleep Stages classification. The common challenge of classification is discussed within a framework of measurements/pre-processing, feature extraction, and classification algorithms for supervised learning. Then, the specific challenges of the 3 applications from a signal processing standpoint are detailed in their specific data processing and ad-hoc classification strategies, focusing on recent trends in the field of activity recognition (multidomain, multi-modal and fusion) and healthcare applications based on vital signs (super-resolution techniques) and commenting on outstanding challenges. To conclude, this paper explores the challenge of the real-time implementation of signal processing/classification algorithms.