  Higher-order interactions (HOIs) are ubiquitous in real-world complex systems
and applications. Investigation of deep learning for HOIs, thus, has become a
valuable agenda for the data mining and machine learning communities. As
networks of HOIs are expressed mathematically as hypergraphs, hypergraph neural
networks (HNNs) have emerged as a powerful tool for representation learning on
hypergraphs. Given the emerging trend, we present the first survey dedicated to
HNNs, with an in-depth and step-by-step guide. Broadly, the present survey
overviews HNN architectures, training strategies, and applications. First, we
break existing HNNs down into four design components: (i) input features, (ii)
input structures, (iii) message-passing schemes, and (iv) training strategies.
Second, we examine how HNNs address and learn HOIs with each of their
components. Third, we overview the recent applications of HNNs in
recommendation, bioinformatics and medical science, time series analysis, and
computer vision. Lastly, we conclude with a discussion on limitations and
future directions.
