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. The dataset is made publicly available at https://cloudsen12.github.io/.