Most existing deblurring methods focus on removing global blur caused by camera shake, while they cannot well handle local blur caused by object movements. To fill the vacancy of local deblurring in real scenes, we establish the first real local motion blur dataset (ReLoBlur), which is captured by a synchronized beam-splitting photographing system and corrected by a post-progressing pipeline. Based on ReLoBlur, we propose a Local Blur-Aware Gated network (LBAG) and several local blur-aware techniques to bridge the gap between global and local deblurring: 1) a blur detection approach based on background subtraction to localize blurred regions; 2) a gate mechanism to guide our network to focus on blurred regions; and 3) a blur-aware patch cropping strategy to address data imbalance problem. Extensive experiments prove the reliability of ReLoBlur dataset, and demonstrate that LBAG achieves better performance than state-of-the-art global deblurring methods and our proposed local blur-aware techniques are effective.