Mt. Fuji is a beautiful example of a stratovolcano, and is almost a perfect symmetric cone (at least when viewed from far away). It is mostly basalt, which is a little bit unusual for stratovolcanoes as most stratovolcanoes are constructed of andesite or dacite compositions. That it is a stratovolcano means that it is composed of layers of both lava and ash. The fact that it is such a beautiful cone probably indicates that it hasn’t recently suffered a big eruption.
“Volcanoes of the World” by Tom Simkin and Lee Seibert lists 63 eruptions of Mt. Fuji since about 9000 years ago. Obviously most of these have been determined by using carbon-14 dating rather than accounts by witnesses. However, the most recent 22 eruptions are listed as having been recorded by people. The most recent eruption was probably the Hōei eruption which started on December 16, 1707 and ended about January 1, 1708. The eruption formed a new crater and a second peak (named Hōei-zan) halfway down its side. Fuji spewed cinders and ash which fell like rain in Izu, Kai, Sagami, and Musashi. Since then, there have been no signs of an eruption.