What's really interesting is the physiological side of dreaming, and the likely causes of lucid dreaming in regards to those. Basically, dreams are the result of a hallucinogenic chemical the body produces during sleep. The chemical's primary purpose appears to be to keep the mind dormant and reduce its ability to control the body at the same time (meaning the body can get properly rested; people who for whatever reason don't have those chemicals properly administered and who toss and turn in their sleep tend to also feel less rested when they wake up than somebody who does not). The chemical also reduces sensory recognition, which has an after-effect when you wake up of your senses being over-powerful. Anyway, dreams are a side-effect of the chemical.
As for lucid dreaming and controlled dreaming, those are basically the mind fighting back against the effects of the chemical. During typical sleep, the mind is both dormant and unaware; this means that while dreams do technically occur, you cannot possibly remember them as your mind is not paying attention. In a normal dream, the conscious mind remains entirely dormant, but aware enough to actually experience the dream. These can be remembered, but usually only briefly, as the mind is not truly attempting to resist the hallucinogen (and thus remains by and large dormant, including in memory function).
The second form, controlled dreaming, is a base-level resistance to the hallucinogen. Your mind resists the illusions brought about in the dreams, even reshaping them to be less unpsetting, but is not able to actually make dreams; the mind is still at the mercy of the hallucinations when this happens. The key difference is that the hallucinations will shift according to input from the dreamer. These kinds of dreams are easier to remember than basic dreams, but still quite easy to forget too, since the brain's resistance to the hallucinogen is not dedicated, but rather sporadic.
The third and most interesting form, lucid dreaming, is full-on resistance to the hallucinogen. The brain wrests control of cognitive functions back, and the result can often startle the dreamer into awakening. When it does not, however, the dreamer will find themselves in a situation where they feel like they are fully awake (as all of their sensory controls come online, even though the body is not responding), and the hallucinogen is providing artificial input for them that they can then guide and shape. I can personally vouch that this kind of dreaming is surreal, simply because you know you're not awake, yet it feels exactly like you are awake. Unfortunately, it's obscenely easy to be woken up in this state too; all it takes is one good unexpected jolt, and you'll be back in the real world.
That about sums it up. I'm sure I don't have the science behind it down perfectly, but it fits pretty well with the actual occurrences of the various forms of dreaming.
Sky Render - Sanity is for the weak.
