In this work, we consider transferring the structure information from large networks to compact ones for dense prediction tasks in computer vision. Previous knowledge distillation strategies used for dense prediction tasks often directly borrow the distillation scheme for image classification and perform knowledge distillation for each pixel separately, leading to sub-optimal performance. Here we propose to distill structured knowledge from large networks to compact networks, taking into account the fact that dense prediction is a structured prediction problem. Specifically, we study two structured distillation schemes: i) pair-wise distillation that distills the pair-wise similarities by building a static graph; and ii) holistic distillation that uses adversarial training to distill holistic knowledge. The effectiveness of our knowledge distillation approaches is demonstrated by experiments on three dense prediction tasks: semantic segmentation, depth estimation and object detection. Code is available at https://git.io/StructKD.