Removing raindrops from a single image is a challenging problem due to the complex changes in shape, scale, and transparency among raindrops. Previous explorations have mainly been limited in two ways. First, publicly available raindrop image datasets have limited capacity in terms of modeling raindrop characteristics (e.g., raindrop collision and fusion) in real-world scenes. Second, recent deraining methods tend to apply shape-invariant filters to cope with diverse rainy images and fail to remove raindrops that are especially varied in shape and scale. In this paper, we address these raindrop removal problems from two perspectives. First, we establish a large-scale dataset named RaindropCityscapes, which includes 11,583 pairs of raindrop and raindrop-free images, covering a wide variety of raindrops and background scenarios. Second, a two-branch Multi-scale Shape Adaptive Network (MSANet) is proposed to detect and remove diverse raindrops, effectively filtering the occluded raindrop regions and keeping the clean background well-preserved. Extensive experiments on synthetic and real-world datasets demonstrate that the proposed method achieves significant improvements over the recent state-of-the-art raindrop removal methods. Moreover, the extension of our method towards the rainy image segmentation and detection tasks validates the practicality of the proposed method in outdoor applications.