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Despite the fact that great progress has been made on single image deraining tasks, it is still challenging for existing models to produce satisfactory results directly, and it often requires a single or multiple refinement stages to gradually improve the quality. However, in this paper, we demonstrate that existing image-level refinement with a stage-independent learning design is problematic with the side effect of over/under-deraining. To resolve this issue, we for the first time propose the mechanism of learning to carry out refinement on the unsatisfactory features, and propose a novel attentive feature refinement (AFR) module. Specifically, AFR is designed as a two-branched network for simultaneous rain-distribution-aware attention map learning and attention guided hierarchy-preserving feature refinement. Guided by task-specific attention, coarse features are progressively refined to better model the diversified rainy effects. By using a separable convolution as the basic component, our AFR module introduces little computation overhead and can be readily integrated into most rainy-to-clean image translation networks for achieving better deraining results. By incorporating a series of AFR modules into a general encoder-decoder network, AFR-Net is constructed for deraining and it achieves new state-of-the-art results on both synthetic and real images. Furthermore, by using AFR-Net as a teacher model, we explore the use of knowledge distillation to successfully learn a student model that is also able to achieve state-of-the-art results but with a much faster inference speed (i.e., it only takes 0.08 second to process a $512\times 512$ rainy image). Code and pre-trained models are available at $\langle $ https://github.com/RobinCSIRO/AFR-Net $\rangle $. [ABSTRACT FROM AUTHOR]