This paper focuses on the research progress and application exploration of graph neural networks (GNNs) in handling heterogeneous graphs, multimodal data, and practical applications. It summarizes various innovative model architectures and learning strategies addressing issues such as semantic aggregation in heterogeneous graphs, representation learning driven by contrastive learning, spectral domain reconstruction, and dynamic graph structure learning in multimodal data. This paper also reviews recent research achievements in practical application problems such as defense against adversarial attacks, calibration of prediction uncertainty, and few-shot learning. Additionally, it explores the wide range of applications of GNNs in fields such as dynamic spatiotemporal data modelling, anomaly detection in multivariate time series, cross-modal data fusion, distributed decision-making in multiagent systems, link prediction and stream data processing, recommendation systems, fake news detection, open-set recognition of mental disorders, avatar rendering, and planning tasks. This paper further analyses the technical trend of integrating GNNs with transformers and discusses current research challenges, such as model scalability, computational efficiency, and the generalizability of defenses against adversarial attacks. It also provides an outlook on future research directions.