Methods and devices are provided for targeted administration of a drug to a patients eye. In one embodiment, the method includes inserting a hollow microneedle into the sclera of the eye at an insertion site and infusing a fluid drug formulation through the inserted microneedle and into the suprachoroidai space of the eye, w herein the infused fluid drug formulation flow s w ithin the suprachoroidai space away from the insertion site during the infusion. The fluid drug formulation may How circumferentially tow ard the retinochoroidal tissue, macula, and optic nerve in the posterior segment of the eye.