Regression-based keypoint localization shows advantages of high efficiency and better robustness to quantization errors than heatmap-based methods. However, existing regression-based methods discard the spatial location prior in input image with a global pooling, leading to inferior accuracy and are limited to single instance localization tasks. We study the regression-based keypoint localization from a new perspective by leveraging the spatial location prior. Instead of regressing on the pooled feature, the proposed Spatial-Aware Regression (SAR) maintains the spatial location map and outputs spatial coordinates and confidence score for each grid, which are optimized with a unified objective. Benefited by the location prior, these spatial-aware outputs can be efficiently optimized, resulting in better localization performance. Moreover, incorporating spatial prior makes SAR more general and can be applied into various keypoint localization tasks. We test the proposed method in 4 keypoint localization tasks including single/multi-person 2D/3D pose estimation, and the whole-body pose estimation. Extensive experiments demonstrate its promising performance, e.g., consistently outperforming recent regressions-based methods.