For many years, text-independent speaker verification research has been dominated by the very successful Gaussian Mixture Model approach. More recently though, several researchers have proposed large margin and kernel approaches to the task, with variable success in international competitions. In this chapter, we aim at presenting the generic framework that has been used by these various kernel approaches for this problem. We will present some of the most successful kernels proposed in the literature and see how one can even learn the kernel. Finally, while it is now clear that kernel approaches, when correctly used, can REACH STATE-OF-THE-ART PERFORMANCE, it is not so clear that the margin plays a decisive role. A discussion on this topic as well as on score normalization adapted to kernel approaches shall conclude the chapter.