Radar-based human motion and activity recognition is currently a topic of great research interest, as the aging population increases and older individuals prefer an independent lifestyle. This technology has a wide range of applications, such as fall detection in assisted living, gesture recognition for human-machine interfaces, and many more. Numerous studies exist on various approaches for radar-based activity capture and classification. However, most of these employ rather artificial data, often obtained in laboratory environments, and typically collected under particular conditions. Specifically, most research so far has aimed at distinguishing a predefined set of single activities with a defined start, stop and duration. This paper aims at drawing the attention to a so far less researched issue, one that will be of vital importance for future real-world application of radar-based human activity recognition: continuous activity recognition, i.e. recognizing specific activities in a stream of several sequential activities with unknown duration and arbitrary transitions between different classes of activities. A review on the current state of the art in this relatively new topic is given, followed by a discussion on future research directions.@en