Spectral clustering is a powerful technique for clustering high-dimensional data, utilizing graph-based representations to detect complex, non-linear structures and non-convex clusters. The construction of a similarity graph is essential for ensuring accurate and effective clustering, making graph structure learning (GSL) central for enhancing spectral clustering performance in response to the growing demand for scalable solutions. Despite advancements in GSL, there is a lack of comprehensive surveys specifically addressing its role within spectral clustering. To bridge this gap, this survey presents a comprehensive review of spectral clustering methods, emphasizing on the critical role of GSL. We explore various graph construction techniques, including pairwise, anchor, and hypergraph-based methods, in both fixed and adaptive settings. Additionally, we categorize spectral clustering approaches into single-view and multi-view frameworks, examining their applications within one-step and two-step clustering processes. We also discuss multi-view information fusion techniques and their impact on clustering data. By addressing current challenges and proposing future research directions, this survey provides valuable insights for advancing spectral clustering methodologies and highlights the pivotal role of GSL in tackling large-scale and high-dimensional data clustering tasks.