There's a initial state that we call the hypnagogic state, that feels almost like REM sleep, or dreaming and then we have stage 2, which takes a long time, and basically is a slowing down of the brain then stages 3 and 4 are now clumped together in the new classification, it's basically what we call slow wave sleep, the Brain is functioning at very low speed with very high amplitude and if you wake people up during that phase, they typically report thoughts, but not dreams and then, REM sleep, or stage 5 here, in which you frequently, at least adults, will report dreams 