As Deep Neural Networks have achieved thrilling breakthroughs in the past decade, data augmentations have garnered increasing attention as regularization techniques when massive labeled data are unavailable. Among existing augmentations, Mixup and relevant data-mixing methods that convexly combine selected samples and the corresponding labels are widely adopted because they yield high performances by generating data-dependent virtual data while easily migrating to various domains. This survey presents a comprehensive review of foundational mixup methods and their applications. We first elaborate on the training pipeline with mixup augmentations as a unified framework containing modules. A reformulated framework could contain various mixup methods and give intuitive operational procedures. Then, we systematically investigate the applications of mixup augmentations on vision downstream tasks, various data modalities, and some analysis \& theorems of mixup. Meanwhile, we conclude the current status and limitations of mixup research and point out further work for effective and efficient mixup augmentations. This survey can provide researchers with the current state of the art in mixup methods and provide some insights and guidance roles in the mixup arena. An online project with this survey is available at https://github.com/Westlake-AI/Awesome-Mixup.