The　problem　of　video　demoireing　is　a　new　challenge　in　video　restoration.　Unlike　image　demoireing,　which　involves　removing　static　and　uniform　patterns,　video　demoireing　requires　tackling　dynamic　and　varied　moire　patterns　while　maintaining　video　details,　colors,　and　temporal　consistency.　It　is　particularly　challenging　to　model　moire　patterns　for　videos　with　camera　or　object　motions,　where　separating　moire　from　the　original　video　content　across　frames　is　extremely　difficult.　Nonetheless,　we　observe　that　the　spatial　distribution　of　moire　patterns　is　often　sparse　on　each　frame,　and　their　long-range　temporal　correlation　is　not　significant.　To　fully　leverage　this　phenomenon,　a　sparsity-constrained　spatial　self-attention　scheme　is　proposed　to　concentrate　on　removing　sparse　moire　efficiently　for　each　frame　without　being　distracted　by　dynamic　video　content.　The　frame-wise　spatial　features　are　then　correlated　and　aggregated　via　the　local　temporal　cross-frame-attention　module　to　produce　temporal-consistent　high-quality　moire-free　videos.　The　above　decoupled　spatial　and　temporal　transformers　constitute　the　Spatio-Temporal　Decomposition　Network,　dubbed　STD-Net.　For　evaluation,　we　present　a　large-scale　video　demoireing　benchmark　featuring　various　real-life　scenes,　camera　motions,　and　object　motions.　We　demonstrate　that　our　proposed　model　can　effectively　and　efficiently　achieve　superior　performance　on　video　demoireing　and　single　image　demoireing　tasks.　The　proposed　dataset　is　released　at　https://github.com/FZU-N/LVDM.