The simulation of condensed matter systems is certainly one of the most appealing perspectives opened by the recent developments in the physics of cold atomic gases. Among the large variety of quantum collective phenomena that one hopes to address with atomic vapours, magnetism is one of the richest. However the quest for the simulation of magnetism immediately raises a challenging question: how can a system of neutral atoms behave as an assembly of charged particles in a magnetic field?The talk will review some promising approaches to answer this question both in a bulk system and in an optical lattice. A first already well-explored path is to rotate the gas and take advantage of the similarity between Lorentz and Coriolis forces. A second possibility is based on the Berry's phase that an atom accumulates when it follows adiabatically one of its internal levels during its motion in a well-chosen energy landscape. In both cases one of the main challenges is to produce atomic states that would be analogous of those characteristic of fractional quantum Hall physics.