The existence of motion blur can inevitably influence the performance of visual object tracking. However, in contrast to the rapid development of visual trackers, the quantitative effects of increasing levels of motion blur on the performance of visual trackers still remain unstudied. Meanwhile, although image-deblurring can produce visually sharp videos for pleasant visual perception, it is also unknown whether visual object tracking can benefit from image deblurring or not. In this paper, we present a Blurred Video Tracking (BVT) benchmark to address these two problems, which contains a large variety of videos with different levels of motion blurs, as well as ground-truth tracking results. To explore the effects of blur and deblurring to visual object tracking, we extensively evaluate 25 trackers on the proposed BVT benchmark and obtain several new interesting findings. Specifically, we find that light motion blur may improve the accuracy of many trackers, but heavy blur usually hurts the tracking performance. We also observe that image deblurring is helpful to improve tracking accuracy on heavily-blurred videos but hurts the performance of lightly-blurred videos. According to these observations, we then propose a new general GAN-based scheme to improve a tracker's robustness to motion blur. In this scheme, a fine-tuned discriminator can effectively serve as an adaptive blur assessor to enable selective frames deblurring during the tracking process. We use this scheme to successfully improve the accuracy of 6 state-of-the-art trackers on motion-blurred videos.