Extreme multilabel classification, which involves predicting a large number of labels among several hundred thousand possible labels, presents significant challenges due to memory constraints, tail labels, and label correlations. Traditional classification methods are not designed to handle such a large number of labels. In this article, different categories of XML algorithms are presented, including compressed sensing, linear algebra-based, and tree-based algorithms, as well as newer deep learning methods. Propensity-based metrics are also discussed to take into account the tail distribution in extreme multilabel classification problems. While deep learning methods have outperformed other XML methods, further exploration of XML methods is needed in a wide range of applications, such as document tagging, product recommendation, and advertising.