In this paper, we explore the emerging role of graph neural networks (GNNs) in optimizing routing for next-generation communication networks. Traditional routing protocols, such as OSPF or the Dijkstra algorithm, often fall short in handling the complexity, scalability, and dynamic nature of modern network environments, including unmanned aerial vehicle (UAV), satellite, and 5G networks. By leveraging their ability to model network topologies and learn from complex interdependencies between nodes and links, GNNs offer a promising solution for distributed and scalable routing optimization. This paper provides a comprehensive review of the latest research on GNN-based routing methods, categorizing them into supervised learning for network modeling, supervised learning for routing optimization, and reinforcement learning for dynamic routing tasks. We also present a detailed analysis of existing datasets, tools, and benchmarking practices. Key challenges related to scalability, real-world deployment, explainability, and security are discussed, alongside future research directions that involve federated learning, self-supervised learning, and online learning techniques to further enhance GNN applicability. This study serves as the first comprehensive survey of GNNs for routing optimization, aiming to inspire further research and practical applications in future communication networks.