Radar is an extremely valuable sensing technology for detecting moving targets and measuring their range, velocity, and angular positions. When people are monitored at home, radar is more likely to be accepted by end-users, as they already use WiFi, is perceived as privacy-preserving compared to cameras, and does not require user compliance as wearable sensors do. Furthermore, it is not affected by lighting conditions nor requires artificial lights that could cause discomfort in the home environment. So, radar-based human activities classification in the context of assisted living can empower an aging society to live at home independently longer. However, challenges remain as to the formulation of the most effective algorithms for radar-based human activities classification and their validation. To promote the exploration and cross-evaluation of different algorithms, our dataset released in 2019 was used to benchmark various classification approaches. The challenge was open from February 2020 to December 2020. A total of 23 organizations worldwide, forming 12 teams from academia and industry, participated in the inaugural Radar Challenge, and submitted 188 valid entries to the challenge. This paper presents an overview and evaluation of the approaches used for all primary contributions in this inaugural challenge. The proposed algorithms are summarized, and the main parameters affecting their performances are analyzed.