The jamming scenario of disordered media, formulated about ten years ago, has in recent years been advanced by analyzing model systems of granular media. This has led to various new concepts that are increasingly being explored a variety of systems. This chapter contains an introductory review of these recent developments and provides an outlook on their applicability to different physical systems and on future directions. The first part of the chapter is devoted to an overview of the findings for model systems of frictionless spheres, focusing on the excess of low‐frequency modes as the jamming point is approached. Particular attention is paid to a discussion of the crossover frequency and length scales that govern this approach. It then discusses the effects of particle asphericity and static friction, the applicability to bubble models for wet foams in which the friction is dynamic, the dynamical arrest in colloids, and the implications for molecular glasses.