Its volcanic activity is currently exhibted only via numerous geothermal vents scattered throughout the region, including the famous Old Faithful Geyser, but within the past two million years it has undergone three extremely large explosive eruptions. The most recent such eruption occurred 640,000 years ago, and spread a layer of volcanic ash over most of the North American continent. Smaller explosive eruptions, similar to the Mount St. Helens eruption, occur every 20,000 years or so; an explosion 13,000 years ago left a 5 kilometer diameter crater at Mary Bay, on the edge of Yellowstone Lake (located in the center of the caldera). As a result of all this activity small earthquakes are common; in 2002 about 2,300 earthquakes were recorded in Yellowstone park. Most of these were too small to be felt by humans.
These eruptions, as well as the continuing geothermal activity, are a result of a large chamber of magma located below the caldera's surface. The magma in this chamber contains gases that are kept dissolved only by the immense pressure that the magma is under. If the pressure is released to a sufficient degree by some geological shift, then some of the gases bubble out and cause the magma to expand. This can cause a runaway reaction of the expansion results in further relief of pressure, for example by blowing crust material off of the top of the chamber, and the result is a very large gas explosion.
A full-scale eruption of the Yellowstone supervolcano could result in millions of deaths locally and catastrophic climactic effects globally. Fortunately there is little indication that such an eruption is imminent in the near future, although study of Yellowstone is ongoing and the system is not yet completely understood. Geologists are closely monitoring the rise and fall of the Yellowstone Plateau, which averages 1.5cm per year, as an indication of changes in magma chamber pressure.
Occasionally proposals are suggested for ways to safely relieve the buildup of dissolved gas in the Yellowstone magma chamber, usually involving drilling holes or using explosives to release small amounts of pressure in a controlled manner. However, none of these ideas are likely to have a noticeable impact. The magma beneath Yellowstone is not very mobile so release of dissolved gases from any given point is not going to do much to the chamber as a whole, and in any event the scale of the problem is far too large for current engineering capabilities to handle.
The Yellowstone hot spot has a long history. Over the past 17 million years or so successive eruptions have flooded lava over wide stretches of Washington, Oregon, California, Nevada, and Idaho, forming a string of comparatively flat calderas linked like beads, as the North American plate moves across the stationary hot spot. The calderas' apparent motion to the east-northeast forms the Snake River Plain. However, what is actually happening is the result of the west-southwest motion of the North American plate with respect to the stationary hot spot deep underneath.