Correctly conveying emotions through facial expressions must have been one of the many most challenging feats an artist must face. Here is my thoughts about this particular issue. Human facial expression is quite complex. Just subtly changing even a single line on the face is enough to alter the entire emotion conveyed. An artist wishing to draw a character's face would need to study and practice how to properly convey every single emotions of that particularly given character. It can take some time to get it right.

Of course, the most expert artists have the ability to recreate every single nuisances of the human face. These are typically artists working professionally in a field where a high degree of realism is required, such as 3D movies, "serious" graphic novels, and so on.

Others, like me, would rather follow a "shortcut" -- This is often used a lot among toon artists and almost every manga cartoonists and in anime series imaginable. It is understandable that conveying a character's facial expression is not an easy task, therefore realism is often disregarded completely; the face is stretched to unrealistic proportions to convey an otherwise too-complex-to-be-drawn expression. The eyes are often the most stretched of all: they can expand or contract, morph into a dollar sign, pink hearts, or if that character is dizzy, spirals. Such usage are usually limited to more comedic situations. In more serious situations, it's still important to at least study correctly how to draw expressions more realistically.

A good way to practice drawing a character's various facial expression is to draw out a huge list of possible expressions for a given character, even the ones the character would least likely use. Generally, I rarely do this myself, but for cartoonists just starting to draw faces correctly, that's my advice to y'all.