We introduce a new attention mechanism, dubbed structural self-attention (StructSA), that leverages rich correlation patterns naturally emerging in key-query interactions of attention. StructSA generates attention maps by recognizing space-time structures of key-query correlations via convolution and uses them to dynamically aggregate local contexts of value features. This effectively leverages rich structural patterns in images and videos such as scene layouts, object motion, and inter-object relations.Using StructSA as a main building block, we develop the structural vision transformer (StructViT) and evaluate its effectiveness on both image and video classification tasks, achieving state-of-the-art results on ImageNet-1K, Kinetics-400, Something-Something V1 & V2, Diving-48, and FineGym.