We propose a fast multi-way spectral clustering algorithm for multi-manifold data modeling. We describe the supporting theory as well as the practical choices guided by it. We emphasize the case of hybrid linear modeling, i.e., when the manifolds are affine subspaces in a Euclidean space, and then extend this setting to more general manifolds and other embedding metric spaces. We exemplify applications of the algorithm to several real-world problems while comparing it with other methods.