High-resolution remote sensing technology for Earth Observation (EO) has radically changed how we monitor the state of our planet around the clock. An effective interpretation of the resulting complex large-scale time series adopts the best machine learning techniques from signal processing, computer vision, pattern recognition, and artificial intelligence. The First Workshop on Complex Data Challenges in Earth Observation was open to both method development and advanced applications in a wide range of related topics, including image and signal processing, gap-filling, data fusion, feature extraction, prediction of spatio-temporal features, and the detection of rules underlying the observed state transitions and causal relationships. The full agenda, featuring keynotes and a selection of high quality contributed talks is available online at www.iarai.ac.at/cdceo21