This paper presents a comprehensive survey on hypergraph neural networks (HNNs), focusing on their design, training, and applications. HNNs are designed to model higher-order interactions (HOIs) in complex systems, which are represented as hypergraphs. The paper provides an in-depth guide to HNNs, covering four key design components: input features, input structures, message-passing schemes, and training strategies. It discusses how HNNs capture HOIs through these components and explores recent applications in recommendation, bioinformatics, medical science, time series analysis, and computer vision. The survey also addresses limitations and future directions for HNN research. The paper highlights the importance of hypergraphs in capturing structural patterns and dynamics in complex systems, and emphasizes the need for effective encoding, training, and application strategies for HNNs. It compares HNNs with traditional graph neural networks (GNNs), noting that HNNs are better suited for modeling HOIs due to their ability to represent complex relationships. The survey concludes with a discussion on the challenges and opportunities in HNN research, emphasizing the need for further exploration in this emerging field.This paper presents a comprehensive survey on hypergraph neural networks (HNNs), focusing on their design, training, and applications. HNNs are designed to model higher-order interactions (HOIs) in complex systems, which are represented as hypergraphs. The paper provides an in-depth guide to HNNs, covering four key design components: input features, input structures, message-passing schemes, and training strategies. It discusses how HNNs capture HOIs through these components and explores recent applications in recommendation, bioinformatics, medical science, time series analysis, and computer vision. The survey also addresses limitations and future directions for HNN research. The paper highlights the importance of hypergraphs in capturing structural patterns and dynamics in complex systems, and emphasizes the need for effective encoding, training, and application strategies for HNNs. It compares HNNs with traditional graph neural networks (GNNs), noting that HNNs are better suited for modeling HOIs due to their ability to represent complex relationships. The survey concludes with a discussion on the challenges and opportunities in HNN research, emphasizing the need for further exploration in this emerging field.