So says Wikipedia: A Lucid Dream Is...
A lucid dream is a dream in which the sleeper is aware that she or he is dreaming. When the dreamer is lucid, she or he can actively participate in and often manipulate the imaginary experiences in the dream environment. Lucid dreams can seem extremely real and vivid depending on a person's level of self-awareness during the lucid dream.[1]
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Lucid dreaming has been researched scientifically, and its existence is well established.[3][4]
Scientific History
...the realization that eye movements performed in dreams affected the dreamer's physical eyes provided a way to prove that actions agreed upon during waking life could be recalled and performed once lucid in a dream. The first evidence of this type was produced in the late 1970s by British parapsychologist Keith Hearne. A volunteer named Alan Worsley used eye movement to signal the onset of lucidity, which were recorded by a polysomnograph machine.Hearne's results were not widely distributed. The first peer-reviewed article was published some years later by Stephen LaBerge at Stanford University, who had independently developed a similar technique as part of his doctoral dissertation.
http://en.wikipedia.org/wiki/Lucid_dream#Scientific_history
