Processes in the magnetized chromosphere of the Sun

We review physical processes in magnetized chromospheres on the Sun. In the quiet chromosphere, it is useful to distinguish between the magnetic network on the boundaries of supergranules, where strong magnetic fields are organized in mainly vertical flux tubes and internetwork regions in the cell interiors, which have traditionally been associated with weak magnetic fields. Recent observations from Hinode, however, suggest that there is a significant amount of horizontal magnetic flux in the cell interior with large field strength. Furthermore, processes that heat the magnetic network have not been fully identified. Is the network heated by wave dissipation and if so, what is the nature of these waves? These and other aspects related to the role of spicules will also be highlighted. A critical assessment will be made on the challenges facing theory and observations, particularly in light of the new space experiments and the planned ground facilities.