Supposedly, people mainly dream during REM sleep, and dreams last up to 20 minutes (see for example the first paragraphs of the Wikipedia article on Dreams).
My subjective experience differs:
No matter at what time I awake, I always awake from a dream.
And since I often awake not on my own (during phases of light sleep) but because I'm disturbed by outside noises (the crying baby of our neighbors, car doors slamming), and often feel groggy and disoriented upon awakening, I probably often awake from deep phases of non-REM sleep. Still, I always awake from a dream.
When I wake up I often remember an unbroken storyline from the last thoughts before I fell asleep until the moment of awakening.
So obviously my dreams must have continued for hours – either in an unbroken stream or by taking up after a break where the story was "paused" before it.
Are there recent theories or research findings that explain this subjective experience?