The problem with trying to do any sort of meaningful research into the way people dream is that it's not exactly easy to give instructions to someone who is asleep. Most of us have no control over what we do when we're sleeping, and limited memories of what we did.
This is where lucid dreamers can come in handy, as researchers from Germany recently discovered. Lucid dreamers are people that have trained themselves to recognize when they enter a dream state, and use that awareness to control what happens (there's a substantial body of work on how to induce a lucid state while sleeping, so Google around if you want more info).
By giving the subjects specific instructions to make a series of left and right hand movements separated by a series of eye movements while asleep, the researchers were able to perform brain scans knowing what was going on in their heads. The eye movements undertaken in dreams are known to show up on an electrooculogram, giving the researchers markers to know what the dreamers were meant to be doing at that point.
fMRI and NIRS scans of the lucid dreamers showed that the areas of the brain associated with doing the proscribed actions in real life were the same that lit up while dreaming about doing them.
So we're not about to jump inside someones innermost REM fantasies, but it's a step towards seeing what goes on people's heads while asleep.