REM and NREM sleep
Sleep has two main types: one in which the eyes move quickly and dreams are vivid, and one that is calm and gets deeper. Through the night the two come in turn.
A little more detail
NREM sleep consists of stages N1, N2 and N3 (slow wave sleep); REM sleep shows rapid eye movements, low-amplitude mixed-frequency EEG and muscle atonia. In adults the cycle repeats about every 90 minutes; N3 is concentrated in the first half of the night and REM in the second half.
Source: Silber MH, Ancoli-Israel S, Bonnet MH et al. The visual scoring of sleep in adults. J Clin Sleep Med. 2007;3(2):121-131. doi:10.5664/jcsm.26814