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There has been rapidly growing demand of polymeric materials coming from different aspects of modern life because of the highly diverse physical and chemical properties of polymers. Polymer informatics is an interdisciplinary research field of polymer science, computer science, information science and machine learning that serves as a platform to exploit existing polymer data for efficient design of functional polymers. Despite many potential benefits of employing a data-driven approach to polymer design, there has been notable challenges of the development of polymer informatics attributed to the complex hierarchical structures of polymers, such as the lack of open databases and unified structural representation. In this study, we review and discuss the applications of machine learning on different aspects of the polymer design process through four perspectives: polymer databases, representation (descriptor) of polymers, predictive models for polymer properties, and polymer design strategy. We hope that this paper can serve as an entry point for researchers interested in the field of polymer informatics., Comment: This is an English translation of the Japanese manuscript published in Proceedings of the Institute of Statistical Mathematics (2021 special issue)