Disclosed are devices and methods for treatment of eye disease such as glaucoma. An implant is placed in the eye wherein the implant provides a fluid pathway for the flow or drainage of aqueous humor from the anterior chamber to the supraciliary or the suprachoroidal space, or to any space in the eye where drainage to that location will lower the intraocular pressure. The implant may include an elongate compressible structure and may be implanted in the eye using a delivery system that folds and or compresses the implant to provide a smaller cross-sectional area to allow a more minimally-invasive procedure. The compressibility of the implant is provided by a porous structure that may be collapsed by compression and delivered through a tube-shaped introducer.