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Moire patterns, appearing as color distortions, severely degrade image and video qualities when filming a screen with digital cameras. Considering the increasing demands for capturing videos, we study how to remove such undesirable moire patterns in videos, namely video demoireing. To this end, we introduce the first hand-held video demoireing dataset with a dedicated data collection pipeline to ensure spatial and temporal alignments of captured data. Further, a baseline video demoireing model with implicit feature space alignment and selective feature aggregation is developed to leverage complementary information from nearby frames to improve frame-level video demoireing. More importantly, we propose a relation-based temporal consistency loss to encourage the model to learn temporal consistency priors directly from ground-truth reference videos, which facilitates producing temporally consistent predictions and effectively maintains frame-level qualities. Extensive experiments manifest the superiority of our model. Code is available at \url{https://daipengwa.github.io/VDmoire_ProjectPage/}.