I'm a bit confused on the many ways eyes can be created

Support Modeling
1

I’ve seen textures placed over a face area with no actual eye geometry. I’m fairly sure this isn’t what I want.

Similarly I have seen iris-pupil textures move across something like a back plane to simulate eyeball movement.

Is this really any different than modeling an eyeball and moving said eyeball?

I suppose what I’m really asking is what are the implications between these methods.

2

Generally you’d make them something like this…

http://www.cgmeetup.net/forums/uploads/gallery/album_838/med_gallery_17603_838_158596.jpg
med_gallery_17603_838_158596.jpg980×527

3

Just note that the human eye isn’t a perfect sphere.
http://images.tutorvista.com/content/human-eye-colourful-world/human-eye-structure.jpeg

4

It all depends on the complexity/realism you want to achieve. The first two methods are very low poly-ish, and may be what you need when your triangle budget is low. The textured plane method I have seen in very stylized eyes (anime/my little pony).

If you’re going for realism, though, you’d model the eyeball.