Abstract Social network alignment (SNA) aims to match corresponding users across different platforms, playing a critical role in cross-platform behavior analysis, personalized recommendations, security, and privacy protection. Traditional methods based on attribute and structural features face significant challenges due to the sparsity, heterogeneity, and dynamic nature of social networks, resulting in limited accuracy and efficiency. Recent advances in graph representation learning (GRL) provide promising solutions to these issues by leveraging deep learning to extract network features, effectively addressing sparsity, integrating heterogeneous data, and adapting to network dynamics. This paper presents a comprehensive survey of SNA methods based on GRL. We first introduce key definitions and outline a framework for SNA using GRL. Next, we systematically review state-of-the-art advancements in both static and dynamic networks, considering homogeneous and heterogeneous settings, including emerging approaches integrating large language models (LLMs). We further conduct an in-depth comparative analysis, highlighting the effectiveness of different GRL-based methods, with a particular emphasis on LLM-enhanced techniques. Finally, we discuss open challenges and outline potential future research directions in this rapidly evolving field.