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Remote measurement of physiological signals from videos is an emerging topic. The topic draws great interest, but the lack of publicly available benchmark databases and a fair validation platform are hindering its further development. The RePSS Challenge is organized as an annual event for this concern. Here the 2nd RePSS is organized in conjunction with ICCV 2021. The 2nd RePSS contains two competition tracks. Track 1 is to measure interbeat-intervals (IBI) from facial videos, which requires accurate measurement of each individual pulse peak. Track 2 is about respiration measurement from facial videos, as respiration is another important physiological index related to both health and emotional status. One new dataset is built and shared for Track 2. This paper presents an overview of the challenge, including data, protocol, results, and discussion. We highlighted the top-ranked solutions to provide insight for researchers, and we also outline future directions for this topic and this challenge.