Same process as for firm cheeses, but pressed even more and consequantly drier. Famous cheeses in this group is Parmigiano Reggiano, Grana Padano, the Swiss Sbrinz and the ewe’s milk cheeses Pecorino and Manchego from Italy and Spain respectively.
Fine for grating as they melts easily. You can of course eat them as they are, but most are used for cooking some way or the other. Some are matured for a long time, and the oldest Parmigiano Reggiano I have tasted was matured for 72 months. If that makes the cheese any better is a topic of constant discussion. At least it makes them different.