One of the things makes Oedipus so remarkable is its emphasis on human complexity and absurdity. It shows how Greeks had struggled to find the true meaning of life and their understanding that human flaws can cause tragic consequences, as seen in this play. (If you haven't read it, Wikipedia does good job explaining : en.wikipedia.org/wiki/Oedipus) Tragic heroes were presented and protagonists and antagonists were characterized. Although they didn't really write happy stories, they knew how to express and elaborate sophisticated ideas. It is interesting to see the majority of today's audience looking for instant and powerful pleasure through different types of art, including literature, while Greeks entertained themselves by talking about the meaning of life and gathering at an amphitheatre and watching tragic plays.
Antigone, the daughter of King Oedipus has been one the most interesting literary characters to me. She defies the corrupted authority and chooses death . Though she was prohibited to bury her brother Polynices, she does so and is about to be punished. However, she ends the tragedy by ending her own life. She is able to distinguish what is "right" and "wrong." And she chooses to do what is right rather than doing what is favorable and beneficial for her.
One of the other interesting thing I could observe is that suicide has been seen as a honorable way to die in Greek culture. When the righteous people are confronted by the corrupt of the society, they tend to kill themselves as a way of resolving the conflict. Socrates drank hemlock and died when he was imprisoned and sentenced to death even though he could easily escape the prison. Like Socrates, the tragic hero Antigone in this play decides to choose "veritas" than compromising with false social structure.
Greeks were great thinkers. They provided the cornerstone of the development of later human societies. Their literary themes can be still agreed and applied to today's world, and their philosophy still impresses us how the core values of human society have been kept consistent over many thousand years. It's hard to know where we are now if we don't know where we were yesterday.