Methods and devices are provided for targeted administration of a drug to a patient's 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 suprachoroidal space of the eye, wherein the infused fluid drug formulation flows within the suprachoroidal space away from the insertion site during the infusion. The fluid drug formulation may flow circumferentially toward the retinochoroidal tissue, macula, and optic nerve in the posterior segment of the eye.