The systematic study of the kernelization framework, whose foretaste we had in Chapter 2 , revealed an intrinsic mathematical richness of this notion. In particular, many classic techniques turn out to be very useful in this context; examples include tools of combinatorial optimization, linear algebra, probabilistic arguments, or results of the graph minors theory. In this chapter, we provide an overview of some of the most interesting examples of more advanced kernelization algorithms. In particular, we provide a quadratic kernel for the Feedback Vertex Set problem. We also discuss the topics of above guarantee parameterizations in the context of kernelization, of kernelization on planar graphs, and of so-called Turing kernelization.