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Data augmentation (DA) is indispensable in modern machine learning and deep neural networks. The basic idea of DA is to construct new training data to improve the model's generalization by adding slightly disturbed versions of existing data or synthesizing new data. This survey comprehensively reviews a crucial subset of DA techniques, namely Mix-based Data Augmentation (MixDA), which generates novel samples by combining multiple examples. In contrast to traditional DA approaches that operate on single samples or entire datasets, MixDA stands out due to its effectiveness, simplicity, flexibility, computational efficiency, theoretical foundation, and broad applicability. We begin by introducing a novel taxonomy that categorizes MixDA into Mixup-based, Cutmix-based, and mixture approaches based on a hierarchical perspective of the data mixing operation. Subsequently, we provide an in-depth review of various MixDA techniques, focusing on their underlying motivations. Owing to its versatility, MixDA has penetrated a wide range of applications, which we also thoroughly investigate in this survey. Moreover, we delve into the underlying mechanisms of MixDA's effectiveness by examining its impact on model generalization and calibration while providing insights into the model's behavior by analyzing the inherent properties of MixDA. Finally, we recapitulate the critical findings and fundamental challenges of current MixDA studies while outlining the potential directions for future works. Different from previous related surveys that focus on DA approaches in specific domains (e.g., CV and NLP) or only review a limited subset of MixDA studies, we are the first to provide a systematical survey of MixDA, covering its taxonomy, methodology, application, and explainability. Furthermore, we provide promising directions for researchers interested in this exciting area.