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The accuracies for many pattern recognition tasks have increased rapidly year by year, achieving or even outperforming human performance. From the perspective of accuracy, pattern recognition seems to be a nearly-solved problem. However, once launched in real applications, the high-accuracy pattern recognition systems may become unstable and unreliable, due to the lack of robustness in open and changing environments. In this paper, we present a comprehensive review of research towards robust pattern recognition from the perspective of breaking three basic and implicit assumptions: closed-world assumption, independent and identically distributed assumption, and clean and big data assumption, which form the foundation of most pattern recognition models. Actually, our brain is robust at learning concepts continually and incrementally, in complex, open and changing environments, with different contexts, modalities and tasks, by showing only a few examples, under weak or noisy supervision. These are the major differences between human intelligence and machine intelligence, which are closely related to the above three assumptions. After witnessing the significant progress in accuracy improvement nowadays, this review paper will enable us to analyze the shortcomings and limitations of current methods and identify future research directions for robust pattern recognition.