I'm an enthusiast, but I wouldn't say that I'm geologically knowledgeable about the current state of affairs. From my visits, I did learn that every autumn, there seems to be a geothermal disturbance with its most noticeable effects around Norris Geyser Basin. This apparently had some significant effects in the last couple of years (one notable one being a renewed cycle of activity for Steamboat Geyser, the world's largest geyser).
The other facts are these: the magma chamber below Yellowstone is active, and there has been uplift observed around the park. One of the most noteworthy examples of that is where the Yellowstone River exits the lake; the uplift has created a series of rapids (Le Hardy Rapids) that the cutthroat trout (which migrate into Yellowstone Lake much like salmon migrate out of the oceans back into rivers) have more difficulty navigating. This has been going on since 1923; more recently there has been a little bit of subsidence (lowering of the surface). Geologists say that this merely indicates that the magma chamber below Yellowstone is active.
When you look at the eruption data, Yellowstone is "due" for a major eruption, but that could probably be said for the next 20,000 years without any significant volcanic activity! Until something really major happens, suffice it to say that Yellowstone is a geothermally active area. And that makes it an amazing place.