Blind video deblurring restores sharp frames from a blurry sequence without any prior. It is a challenging task because the blur due to camera shake, object movement and defocusing is heterogeneous in both temporal and spatial dimensions. Traditional methods train on datasets synthesized with a single level of blur, and thus do not generalize well across levels of blurriness. To address this challenge, we propose a dual attention mechanism to dynamically aggregate temporal cues for deblurring with an end-to-end trainable network structure. Specifically, an internal attention module adaptively selects the optimal temporal scales for restoring the sharp center frame. An external attention module adaptively aggregates and refines multiple sharp frame estimates, from several internal attention modules designed for different blur levels. To train and evaluate on more diverse blur severity levels, we propose a Challenging DVD dataset generated from the raw DVD video set by pooling frames with different temporal windows. Our framework achieves consistently better performance on this more challenging dataset while obtaining strongly competitive results on the original DVD benchmark. Extensive ablative studies and qualitative visualizations further demonstrate the advantage of our method in handling real video blur.