With each blink, the eyelids sweep across the eye, spreading the tear film evenly across the surface. The blinking motion of the eyelids forces the tears into tiny drains found at the inner corners of the upper and lower eyelids. The tear film travels from the puncta into the upper and lower canaliculus, which empty into the lacrimal sac. The lacrimal sac drains into the nasolacrimal duct which connects to the nasal passage. This connection between the tear production system and the nose is the reason your nose runs when you cry.
Some patients can actually taste eye drops as they drain from the nasal passage into the throat.