Rain streaks and raindrops are two natural phenomena, which degrade image capture in different ways. Currently, most existing deep deraining networks take them as two distinct problems and individually address one, and thus cannot deal adequately with both simultaneously. To address this, we propose a Dual Attention-in-Attention Model (DAiAM) which includes two DAMs for removing both rain streaks and raindrops. Inside the DAM, there are two attentive maps - each of which attends to the heavy and light rainy regions, respectively, to guide the deraining process differently for applicable regions. In addition, to further refine the result, a Differential-driven Dual Attention-in-Attention Model (D-DAiAM) is proposed with a "heavy-to-light" scheme to remove rain via addressing the unsatisfying deraining regions. Extensive experiments on one public raindrop dataset, one public rain streak and our synthesized joint rain streak and raindrop (JRSRD) dataset have demonstrated that the proposed method not only is capable of removing rain streaks and raindrops simultaneously, but also achieves the state-of-the-art performance on both tasks.