Genito-urinary function
Sleep-related erections (nocturnal penile tumescence) develop rapidly during REM sleep, and may persist into NREM sleep.

Their frequency is not affected by sexual abstinence or activity. There is little change in their frequency with age, even in the elderly, and they may occur in prepubertal children.

Endocrine function
This is considerably different during REM sleep compared to NREM sleep or wakefulness.

Immunological function
This is different during sleep compared to wakefulness, but there are no known specific effects of REM sleep.

References