This paper presents a survey of kernel and spectral clustering methods. The focus is on partitioning clustering with special attention to kernel and spectral methods. The aim is to present a survey of kernel and spectral clustering methods, two approaches that can produce nonlinear separating hypersurfaces between clusters. Kernel clustering methods are the kernel versions of classical clustering algorithms such as K-means, SOM, and Neural Gas. Spectral clustering arises from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof is given that these two paradigms have the same mathematical foundation. Fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering. The paper also discusses the equivalence between spectral and kernel clustering methods, and provides a comparison of some spectral clustering methods. Applications of these methods are also discussed, including image segmentation, handwritten digit recognition, face recognition, speech recognition, and prediction of crop yield. The paper concludes with a summary of the key concepts and methods in kernel and spectral clustering.This paper presents a survey of kernel and spectral clustering methods. The focus is on partitioning clustering with special attention to kernel and spectral methods. The aim is to present a survey of kernel and spectral clustering methods, two approaches that can produce nonlinear separating hypersurfaces between clusters. Kernel clustering methods are the kernel versions of classical clustering algorithms such as K-means, SOM, and Neural Gas. Spectral clustering arises from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof is given that these two paradigms have the same mathematical foundation. Fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering. The paper also discusses the equivalence between spectral and kernel clustering methods, and provides a comparison of some spectral clustering methods. Applications of these methods are also discussed, including image segmentation, handwritten digit recognition, face recognition, speech recognition, and prediction of crop yield. The paper concludes with a summary of the key concepts and methods in kernel and spectral clustering.