The paper provides a comprehensive review of advancements in representation learning on graphs, focusing on methods that automatically learn low-dimensional embeddings to encode graph structure. The authors highlight the importance of incorporating graph structure into machine learning models, which is crucial for tasks such as link prediction and node classification. Traditional approaches relied on user-defined heuristics, while recent methods use deep learning and nonlinear dimensionality reduction techniques. The review covers matrix factorization-based methods, random-walk based algorithms, and graph neural networks, emphasizing their applications and future directions. The paper also introduces a unified framework to describe these approaches and discusses their extensions to multi-modal graphs and task-specific supervision.The paper provides a comprehensive review of advancements in representation learning on graphs, focusing on methods that automatically learn low-dimensional embeddings to encode graph structure. The authors highlight the importance of incorporating graph structure into machine learning models, which is crucial for tasks such as link prediction and node classification. Traditional approaches relied on user-defined heuristics, while recent methods use deep learning and nonlinear dimensionality reduction techniques. The review covers matrix factorization-based methods, random-walk based algorithms, and graph neural networks, emphasizing their applications and future directions. The paper also introduces a unified framework to describe these approaches and discusses their extensions to multi-modal graphs and task-specific supervision.