Often, we wake up in the mornings and cannot remember our dreams. Or, if we can remember them, it's only the last dream before waking up, and only fragments of it, despite the fact that we generally have several dreams every night. This happens both in deep sleep and REM sleep, with dreams in the REM phase being more vivid, visual and emotional.
If you would like to train yourself to remember your dreams better, there are a few small tools you can try. In many cases, we become better at remembering dreams if, the night before, we say often enough that we would like to remember our final dream before waking up the next morning. A notepad on the bedside table to write things down can also help. Even saying what you would like to dream about, on the evening before sleep, can work. In some cases, certain solutions to problems can also come to you in your sleep, which you would not have thought of during the course of the day.
These insights can even be applied to nightmares too. Think through a good ending for your nightmare and say it to yourself again and again. After a certain period of time, your dreams will often in fact turn into the good ending and disappear.
Source: Schlafen für Aufgeweckte, Dr. med. Michael Feld, 3. Auflage 2015