Reference-based Super-Resolution (Ref-SR) has recently emerged as a promising paradigm to enhance a low-resolution (LR) input image or video by introducing an additional high-resolution (HR) reference image. Existing Ref-SR methods mostly rely on implicit correspondence matching to borrow HR textures from reference images to compensate for the information loss in input images. However, performing local transfer is difficult because of two gaps between input and reference images: the transformation gap (e.g., scale and rotation) and the resolution gap (e.g., HR and LR). To tackle these challenges, we propose -Matching in this work, which performs explicit robust matching crossing transformation and resolution. 1) To bridge the transformation gap, we propose a contrastive correspondence network, which learns transformation-robust correspondences using augmented views of the input image. 2) To address the resolution gap, we adopt teacher-student correlation distillation, which distills knowledge from the easier HR-HR matching to guide the more ambiguous LR-HR matching. 3) Finally, we design a dynamic aggregation module to address the potential misalignment issue between input images and reference images. In addition, to faithfully evaluate the performance of Reference-based Image Super-Resolution (Ref Image SR) under a realistic setting, we contribute the Webly-Referenced SR (WR-SR) dataset, mimicking the practical usage scenario. We also extend -Matching to Reference-based Video Super-Resolution (Ref VSR) task, where an image taken in a similar scene serves as the HR reference image. Extensive experiments demonstrate that our proposed -Matching significantly outperforms state of the arts by up to 0.7 dB on the standard CUFED5 benchmark and also boosts the performance of video super-resolution by incorporating the -Matching component into Video SR pipelines. Notably, -Matching also shows great generalizability on WR-SR dataset as well as robustness across large scale and rotation transformations. Codes and datasets are available at https://github.com/yumingj/C2-Matching .