Edge detection has made significant progress with the help of deep Convolutional Networks (ConvNet). These ConvNet based edge detectors have approached human level performance on standard benchmarks. We provide a systematical study of these detector outputs. We show that the detection results did not accurately localize edge pixels, which can be adversarial for tasks that require crisp edge inputs. As a remedy, we propose a novel refinement architecture to address the challenging problem of learning a crisp edge detector using ConvNet. Our method leverages a top-down backward refinement pathway, and progressively increases the resolution of feature maps to generate crisp edges. Our results achieved superior performance, surpassing human accuracy when using standard criteria on BSDS500, and largely outperforming state-of-the-art methods when using more strict criteria. More importantly, we demonstrate the benefit of crisp edge maps for several important applications in computer vision, including optical flow estimation, object proposal generation and semantic segmentation.