I often hear about how people can control their sleep and then remember everything that happened before, and so on. Is it real? And if so, how to do it?

hospade, home-grown mystics, you have no control. castaneda, dream catchers, what else do you suggest? I must say, I read the castaneda. and I have a dreamcatcher hanging, albeit for purely decorative purposes. however, I assure you, you can even flip through castaneda until you turn blue, sitting under the dream catcher, but this will not bring you closer to the state described by the author of the question, and called a lucid dream. because this technique does not at all belong to the field of mysticism and other crazy magic rituals, but is a very real meditative practice, and the mechanism itself has a scientific explanation. Moreover, now on the Internet special electronic gizmos are even sold, designed to facilitate the entry into a state of lucid dreaming. and on request "lucid dreaming" Google will give out an exhaustive amount of information. quite interesting, by the way, writes about this ken wilber, for those interested I recommend

This is real. For me, for example, this does not always happen. Sometimes I see a dream in reality and in life, when this moment is repeated, I know what to do and what will happen next. It's scary at first, but now I'm reading Carlos Castaneda.
And I advise you (:

Yes, it's real. I myself have this ability) Few people give it at birth. To get this ability, try hanging an owl feather dreamcatcher.