They both run bilaterally down the neck and thorax. Right vagus/left vagus; right phrenic/left phrenic. Vagus n. runs inside the carotid sheath with the common carotid artery(and internal carotid artery), internal jugular vein and deep cervical lymph nodes on each side. Some people remember this by thinking "CVI" for the contents of the carotid sheath minus the lymph nodes. To remember the origin of the phrenic nerves, think "C3-C4-C5 Keeps you alive" i.e. breathing, even though it originates primarily from the C4 root, and the left phrenic nerve pierces the diaphragm.