In the last decade, new indirect imaging techniques have been proposed to unveil the surface magnetic topologies of rapidly rotating active stars, which are found to be vastly different from that of the Sun. After a quick recall of how direct magnetic field (i.e. spectropolarimetric) signatures can be detected in such stars, I describe in detail to which extent surface magnetic field topologies can be recovered from extensive sets of time resolved, high signal to noise Zeeman signatures. I outline in particular how specific assumptions on the field structure (e.g. potential field, linear force-free field) can help improving the modelling, not only of the surface field map, but also of the large scale topology of the coronal field. I finally present the results obtained to date on how dynamo processes seem to operate in the atmospheres of cool active stars and how they differ from those of the Sun.