The lacrimal implant delivery systems and methods described herein provide for controlled release of a therapeutic agent for the treatment of disease, including the treatment of glaucoma, ocular hypertension, or elevated intraocular pressure with latanoprost or other anti-glaucoma agents. Treatment of disease, including glaucoma, ocular hypertension, or elevated intraocular pressure with latanoprost or other anti-glaucoma agent in conjunction with penetration enhancer, such as benzalkonium chloride, and/or artificial tears is also provided. Also provided are implants containing a drug core emplacable in a punctum adjacent to an eye of a patient for controlled release of a therapeutic agent such as latanoprost for the treatment of glaucoma, the drug core containing a polymer such as cross-linked silicone, a therapeutic agent, and an excipient, wherein the excipient can increase the rate of release of the agent from the drug core, or can increase the drug loading in the core without loss of desirable homogeneity of the agent within the core, or can improve retention of the agent in the eye or in tear fluid, or can increase corneal penetration of the agent into the eye.