According to Bryn Mawr College, the pons is largely responsible for dreaming because of its role in regulating REM sleep, which is vital for dreaming. Damage to the pons can result in loss of dreaming sleep.
Other areas of the brain that are involved in dreams indirectly include the prefrontal cortex and the frontal lobes, which contain large fiber pathways that carry the neurotransmitter dopamine. Increased dopamine activity is known to increase dreaming activity, which is demonstrated through use of dopaminergic stimulants, such as L-dopa. While dreaming is complex and not fully understood, the pons, prefrontal cortex and frontal lobes are known to be deeply involved.