This paper provides a comprehensive survey of kernel and spectral clustering methods, focusing on their ability to produce nonlinear separating hypersurfaces between clusters. The authors present both classical partitioning clustering methods (such as K-means, SOM, and Neural Gas) and their kernelized versions, as well as spectral clustering methods rooted in spectral graph theory. The paper highlights the equivalence between these two approaches, demonstrating that they share the same mathematical foundation. Key concepts such as kernel functions, Mercer kernels, and the Laplacian matrix are discussed in detail. The paper also explores various applications of these methods, including image segmentation, handwritten digit recognition, and bioinformatics. Additionally, it introduces fuzzy and possibilistic clustering methods, which extend the notion of membership to clusters, allowing for more flexible and robust clustering solutions. The paper concludes with a discussion on the theoretical and practical aspects of these clustering techniques, emphasizing their effectiveness in handling complex data structures.This paper provides a comprehensive survey of kernel and spectral clustering methods, focusing on their ability to produce nonlinear separating hypersurfaces between clusters. The authors present both classical partitioning clustering methods (such as K-means, SOM, and Neural Gas) and their kernelized versions, as well as spectral clustering methods rooted in spectral graph theory. The paper highlights the equivalence between these two approaches, demonstrating that they share the same mathematical foundation. Key concepts such as kernel functions, Mercer kernels, and the Laplacian matrix are discussed in detail. The paper also explores various applications of these methods, including image segmentation, handwritten digit recognition, and bioinformatics. Additionally, it introduces fuzzy and possibilistic clustering methods, which extend the notion of membership to clusters, allowing for more flexible and robust clustering solutions. The paper concludes with a discussion on the theoretical and practical aspects of these clustering techniques, emphasizing their effectiveness in handling complex data structures.