Ophthalmic drug for the anterior chamber diseases are delivered into tears by either eye drops or by extended release devices placed in the eyes. The instilled drug exits the eye through various routes including tear drainage into the nose through the canaliculi and transport across various ocular membranes. Understanding the mechanisms relevant to each route can be useful in predicting the dependency of ocular bioavailability on various formulation parameters, such as drug concentration, salinity, viscosity, etc. Mathematical modeling has been developed for each of the routes and validated by comparison with experiments. The individual models can be combined into a system model to predict the fraction of the instilled drug that reaches the target. This review summarizes the individual models for the transport of drugs across the cornea and conjunctiva and the canaliculi tear drainage. It also summarizes the combined tear dynamics model that can predict the ocular bioavailability of drugs instilled as eye drops. The predictions from the individual models and the combined model are in good agreement with experimental data. Both experiments and models predict that the corneal bioavailability for drugs delivered through eye drops is less than 5% due to the small area of the cornea in comparison to the conjunctiva, and the rapid clearance of the instilled solution by tear drainage. A contact lens is a natural choice for delivering drugs to the cornea due to the placement of the contact in the immediate vicinity of the cornea. The drug released by the contact towards the cornea surface is trapped in the post lens tear film for extended duration of at least 30min allowing transport of a large portion into the cornea. The model predictions backed by in vivo animal and clinical data show that the bioavailability increases to about 50% with contact lenses. This realization has encouraged considerable research towards delivering ocular drugs by contact lenses. Commercial contacts are, however, not ideal for drug delivery due to the short release durations which may necessitate wearing multiple lenses each day, reducing the viability of this approach. Recent research has focused on designing contacts that retain all critical properties while increasing the release durations to a few hours or a few days. Beagle dog studies with contact lenses containing vitamin E nanobarriers to attenuate drug transport have shown promising results. Human studies using contacts for drug delivery have also been conducted for allergy therapy but drug eluting contacts are not available in the market for any therapy.