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Solar and lunar eclipses are pretty straightforward. But what about eclipses when you are standing on the Moon? I have been trying to Google the info, but there's some gaming clan that has taken the name "terran eclipse" so it's hard to find the real stuff.
I was able to find this article on lunar eclipse from the Moon (the Earth eclipsing the sun). But what about the other way - a solar eclipse observed from the Moon? What would Earth look like? Would anything special be happening on the Moon?
As Wayfaring Stranger's answer says, during a lunar eclipse seen from Earth, an observer on the Moon would see a solar eclipse. Earth is about 4 times the apparent diameter of the Sun. You can see a photo of such an eclipse, taken by Japan's Kaguya spacecraft in lunar orbit, here.
During a solar eclipse seen from Earth, an observer on the Moon would see the Moon's shadow on the surface of Earth. I don't know of any photos of such a shadow as seen from the Moon, but here's a photo of a solar eclipse seen from the Mir space station in 1999.
+1 also asked and answered in Space SE: Have there been any photos taken of a total Earth-Sun eclipse from the Moon, or its vicinity?
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A lunar eclipse on earth is a solar eclipse on the moon. The earth takes up 2° of sky from the lunar surface (vs 0.5°), so you'd see less corona in your space suit. The moon's speed through earth's shadow is only about 1 km per second, so you'd have up to 107 minutes of totality. What with earth's atmosphere, I doubt you'd see much in the way of Baily's beads, but there'd likely be a spectacular round the world sunset glow to make up for that.
