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In this article, we present an overview of computational approaches to lexical complexity prediction focusing on the work carried out on English data. We survey relevant approaches to this problem which include traditional machine learning classifiers (e.g., SVMs, logistic regression) and deep neural networks as well as a variety of features, such as those inspired by literature in psycholinguistics as well as word frequency, word length, and many others. Furthermore, we introduce readers to past competitions and available datasets created on this topic. 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