In this paper, we propose a novel approach, called EvDistill, to learn a student network on the unlabeled and unpaired event data (target modality) via knowledge distillation (KD) from a teacher network trained with large labeled image data (source modality). To enable KD across the unpaired modalities, we first propose a bidirectional modality reconstruction (BMR) module to bridge both modalities and simultaneously exploit them to distill knowledge via the crafted pairs, causing no extra computation in the test time. The BMR is improved by the end-task and KD losses in an end-to-end manner. Second, we leverage the structural similarities of both modalities and adapt the knowledge by matching their distributions. Moreover, as most prior feature KD methods are unimodality and less applicable to our problem, we propose an affinity graph KD and other losses to boost the distillation. Our extensive experiments on semantic segmentation and object recognition demonstrate that EvDistill achieves significantly better results than the prior works and KD with only events and APS frames.