The right recurrent laryngeal arises from the vagus nerve as it passes in front of the right subclavian artery. It then curves below and behind the subclavian artery and angles slightly medially, as it courses superiorly, behind the thyroid gland toward the larynx.
The left recurrent laryngeal nerve arises from the vagus trunk, as it passes in front of the aortic arch. The recurrent laryngeal then passes below and behind the aorta, at the level of the ligamentum arteriosum. Finally, it ascends within the visceral compartment of the neck, behind the thyroid gland, between the esophagus and trachea.
Picture of the right recurrent laryngeal nerve passing in the groove between the trachea and the esophagus (the gutter), as it ascends toward the larynx.