"Dreams can come true," sang Gabrielle, and she was closer to the truth than she knew according to a fascinating insight into dreams and dreaming served up by the third instalment in the latest series of Horizon, which is rapidly shaping up to be one of the best series of recent years. So whether you're inventing the sewing machine, rehearsing for that important meeting, or listening out for subliminal messages about the state of your marriage, dreams can help.

I expected the first section of this programme to be spent explaining what dreaming is and when it happens - you know, the old "deep sleep; REM sleep; non-REM sleep" thing - but what I hadn't realised is that latest research shows we dream during non-REM sleep as well as REM sleep.

And even more fascinating is that the kind of dreams we dream differ between the two. In non-REM sleep, you experience those dreams connected to positive feelings about yourself. But during REM sleep, the amygdala is much more active. This is the part of the brain that deals with memories of traumas and nasty experiences, so REM sleep dreaming tends to concentrate on negative feelings and bad experiences. So much so that it's been shown that people with depressive personalities spend too much time in REM sleep, and this could be one factor in their being depressed in the first place!

Dreams originate in the parietal lobe, and stroke patients who suffer damage to this area of the brain often experience an inability to dream which upsets their sleep patterns. It's almost as if the brain "expects" to be dreaming, and when sufferers initially leave deep sleep and can't dream, they wake up. This has led some scientists to hypothesise that dreaming is a way of keeping us asleep.

But why would that be beneficial? Because the power of dreams can spill over into our waking lives. Experiments have shown a link between regular dreaming of certain events and the subsequent experiencing of similar events in real life. It came as no surprise to researchers to learn that a man who dreamt of bad experiences with women for more than the average, went on to get a divorce. It's also been demonstrated that learning a new skill - such as playing a video game - will lead the brain to rerun the experience in dreams and try to match it with existing memories. The result is that the next time you come to play the game, you are better equipped to deal with whatever scenario is on offer.

In a similar way, childish dreams about encounters with monsters and wild animals are a throwback to a time when humans were likely to encounter such things during their waking lives. Dreams are, effectively, rehearsals for these real-life events. As we mature, the wild animals are replaced by elements from working and social life that we benefit from practising. And if the mind is preoccupied with a puzzle or problem, dreams have been known on many occasions to help with the answer. The inventor of the sewing machine, unable to figure out how to attach the thread to the needle, famously dreamt of natives throwing spears that had holes at their tips, and there are many other examples of inventions, or works of artistic or literary merit - such as Mary Shelley's Frankenstein - the ideas for which came to the artist in a dream.

Finally, Horizon touched on the subject of "lucid dreaming" - a trick where the dreamer can become aware that they're dreaming, and begin to direct the dream. If this has ever happened to you, you'll know how exciting it can be to wield ultimate power in a dreamworld where nothing is impossible. Some people can do this naturally, others can be trained to do it, and it turns out that for those suffering from depression or anxiety, the feelings of power it engenders can be very therapeutic.

This totally absorbing programme flitted from one area of dream research to another, each more fascinating than the last. My imagination was captured by the idea of the dream database, where the researcher is recording common dream sequences and events in an attempt to extract patterns and interpretations with a scientific basis to explain what dreams actually mean. But it was the lucid dreaming that really pushed my buttons. I think I'll be asking my missus to flash a torch into my face tonight. If I can wake her up.