Understanding the cause of magnetospheric substorms is a challenging problem in space physics but is also very rewarding since it relates to many energetic phenomena in the Earth's magnetosphere and to other impulsive energetic events in space plasmas. Substorm models can be classified into four different categories, namely: (1) internally triggered or externally driven processes in the near-Earth magnetosphere region, (2) magnetic reconnection in the mid-tail region, (3) coupling between the ionosphere and magnetosphere, and (4) simplified or abstract description of the magnetospheric system. The first category includes a rich variety of macro- and micro-instabilities (ballooning, cross-field current, lower hybrid drift, entropy anti-diffusion, and parallel current driven instabilities). This category is the most promising one since it can naturally account for several observational constraints on the substorm onset process. In particular, the model invoking a combination of the kinetic ballooning and the cross-field current instabilities is described, together with results from particle simulation on this mechanism. Crucial elements of substorm models in the other three categories are synthesized into this model as well.This article was scheduled to appear in issue 5 of Plasma Phys. Control. Fusion. To access this Special issue please follow this link: http://www.iop.org/EJ/toc/0741-3335/45/5