Abstract: In the problem of manifold learning, one seeks to find a smooth low-dimensional manifold embedded in the high-dimensional vector space, based on a set of sample points. Spectral graph theory studies the eigenvectors and eigenvalues of matrices associated with graphs and has been widely used in the manifold learning algorithm recently. In this paper, the relationship between the manifold and the manifold learning is introduced first, and then some typical manifold learning algorithms based on spectral graph theory are studied. Finally, some directions for further research are suggested.