This paper provides a comprehensive survey on Hypergraph Neural Networks (HNNs), focusing on their architecture, training strategies, and applications. HNNs are designed to capture higher-order interactions (HOIs) in complex systems, which are prevalent in various domains such as physics, biology, and social networks. The authors break down HNNs into four key components: input features, input structures, message-passing schemes, and training strategies. They then detail how these components address HOIs and discuss recent applications in recommendation systems, bioinformatics, medical science, time series analysis, and computer vision. The paper concludes with a discussion on limitations and future directions, emphasizing the need for more theoretical investigations and the development of HNNs for complex hypergraphs.This paper provides a comprehensive survey on Hypergraph Neural Networks (HNNs), focusing on their architecture, training strategies, and applications. HNNs are designed to capture higher-order interactions (HOIs) in complex systems, which are prevalent in various domains such as physics, biology, and social networks. The authors break down HNNs into four key components: input features, input structures, message-passing schemes, and training strategies. They then detail how these components address HOIs and discuss recent applications in recommendation systems, bioinformatics, medical science, time series analysis, and computer vision. The paper concludes with a discussion on limitations and future directions, emphasizing the need for more theoretical investigations and the development of HNNs for complex hypergraphs.