As a natural extension of link prediction on graphs, hyperlink prediction aims for the inference of missing hyperlinks in hypergraphs, where a hyperlink can connect more than two nodes. Hyperlink prediction has applications in a wide range of systems, from chemical reaction networks and social communication networks to protein-protein interaction networks. In this article, we provide a systematic and comprehensive survey on hyperlink prediction. We adopt a classical taxonomy from link prediction to classify the existing hyperlink prediction methods into four categories: similarity-based, probability-based, matrix optimization-based, and deep learning-based methods. To compare the performance of methods from different categories, we perform a benchmark study on various hypergraph applications using representative methods from each category. Notably, deep learning-based methods prevail over other methods in hyperlink prediction.