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Given the importance of catalysts in the chemical industry, they have been extensively investigated by experimental and numerical methods. With the development of computational algorithms and computer hardware, large-scale simulations have enabled influential studies with more atomic details reflecting microscopic mechanisms. This review provides a comprehensive summary of recent developments in molecular dynamics, including ab initio molecular dynamics and reaction force-field molecular dynamics. Recent research on both approaches to catalyst calculations is reviewed, including growth, dehydrogenation, hydrogenation, oxidation reactions, bias, and recombination of carbon materials that can guide catalyst calculations. Machine learning has attracted increasing interest in recent years, and its combination with the field of catalysts has inspired promising development approaches. Its applications in machine learning potential, catalyst design, performance prediction, structure optimization, and classification have been summarized in detail. This review hopes to shed light and perspective on ML approaches in catalysts. [ABSTRACT FROM AUTHOR]