Guided filter is a fundamental tool in computer vision and computer graphics, which aims to transfer structure information from the guide image to the target image. Most existing methods construct filter kernels from the guidance itself without considering the mutual dependency between the guidance and the target. However, since there typically exist significantly different edges in two images, simply transferring all structural information from the guide to the target would result in various artifacts. To cope with this problem, we propose an effective framework named deep attentional guided image filtering, the filtering process of which can fully integrate the complementary information contained in both images. Specifically, we propose an attentional kernel learning module to generate dual sets of filter kernels from the guidance and the target and then adaptively combine them by modeling the pixelwise dependency between the two images. Meanwhile, we propose a multiscale guided image filtering module to progressively generate the filtering result with the constructed kernels in a coarse-to-fine manner. Correspondingly, a multiscale fusion strategy is introduced to reuse the intermediate results in the coarse-to-fine process. Extensive experiments show that the proposed framework compares favorably with the state-of-the-art methods in a wide range of guided image filtering applications, such as guided super-resolution (SR), cross-modality restoration, and semantic segmentation. Moreover, our scheme achieved the first place in the real depth map SR challenge held in ACM ICMR 2021. The codes can be found at https://github.com/zhwzhong/DAGF.