Our location within the thin disk of the Milky Way allows studies of Galactic objects, like supernova remnants and HII regions, as well as the structure and composition of the interstellar medium in much more detail than in any other galaxy. Synchrotron emission at low frequencies originates from low-energy electrons, which escaped from their origin in supernova remnants in the Galactic disk into the weak halo magnetic field a long time ago. Details of this propagation and evolution process will be investigated with LOFAR. At low frequencies a small amount of Faraday rotation already causes a significant change of the polarisation angle with frequency. LOFAR will make the investigation of the distribution of small clumps of thermal electrons and their relation to turbulent weak magnetic fields possible, which are of high interest to understand the polarisation properties of the interstellar medium in general. The increase of thermal absorption and of depolarisation by Faraday rotation at low frequencies will be used to model the distribution of emission along the line-of-sight, leading to a three-dimensional model of the gas and magnetic fields in the Milky Way. These results are of high importance to understand nearby galaxies where the spatial resolution is much lower. Finally, the emission of the Milky Way is a foreground for all kinds of sensitive extragalactic observations and must be properly separated for a correct interpretation of these data.