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Accurately characterizing clouds and their shadows is a long-standing problem in the Earth Observation community. Recent works showcase the necessity to improve cloud detection methods for imagery acquired by the Sentinel-2 satellites. However, the lack of consensus and transparency in existing reference datasets hampers the benchmarking of current cloud detection methods. Exploiting the analysis-ready data offered by the Copernicus program, we created CloudSEN12, a new multi-temporal global dataset to foster research in cloud and cloud shadow detection. CloudSEN12 has 49,400 image patches, including (1) Sentinel-2 level-1C and level-2A multi-spectral data, (2) Sentinel-1 synthetic aperture radar data, (3) auxiliary remote sensing products, (4) different hand-crafted annotations to label the presence of thick and thin clouds and cloud shadows, and (5) the results from eight state-of-the-art cloud detection algorithms. At present, CloudSEN12 exceeds all previous efforts in terms of annotation richness, scene variability, geographic distribution, metadata complexity, quality control, and number of samples.