A glaucoma drainage device includes an elongated body extending axially from a distal end to a proximal end. The distal end forms a wedge with a leading distal edge. During implantation of the device into the suprachoroidal space of the eye, the wedge can facilitate penetration into and spreading open the tissue of the suprachoroidal space. The elongate body has one or more outer surfaces that define at least one open groove extending from at or near the proximal end towards the distal end of the body. With the distal end of the elongate body located in the suprachoroidal space of the eye and the distal end of the elongate body extending into the anterior chamber of the eye, the at least one open groove is configured such that aqueous humor flows along the open groove from the anterior chamber of the eye to the suprachoroidal space of the eye.
