Surgical methods and related devices for treating glaucoma are described. The methods include trabecular bypass surgery, which involve bypassing diseased trabecular meshwork with a seton implant. The implant is used to limit a healing process known as filling in, which has a tendency to close surgically created openings in the trabecular meshwork. In addition to bypassing the diseased trabecular meshwork, existing outflow pathways are also used or restored. The seton implant is positioned through the trabecular meshwork so that an inlet end of the seton implant is exposed to the anterior chamber of the eye and an outlet end is positioned into fluid collection channels at about an exterior surface of the trabecular meshwork or up to the level of aqueous veins.