Oedipus the King (also called Oedipus Rex) is relevant to the world today in two main ways. First, it is a perfect illustration of Freud's theory of the Oedipal conflict, which states that a young boy desires to kill his father and marry his mother, but represses these desires into his unconscious mind so that he can join the social order. Oedipus enacts this exact scenario, and engages in an act of repression when, knowing the prophecy, it never once crosses his mind that the man he killed on the road might be his father, and the older woman he marries his mother, until he begins to investigate the causes of the plague. The play, therefore, becomes food for thought about the unconscious impulses that drive us, a theme that fascinates the modern world.
Second, while the ideas of Greek gods controlling our destinies may seem quaint, there is a great deal of relevance to the idea that we must accommodate ourselves to large forces in the universe. While the wealthy and powerful, for example, might want to control the destiny of the planet and deny (as Oedipus and Jocasta do) the power of larger forces, in the end, forces (such as climate change) will bring a "plague" to the Earth—just as Oedipus' defiance of the gods brings a plague to Thebes. The play warns that the powerful ignore or defy these forces at their peril, and that the peril first shows itself in the fate of the little people. The play also shows us that if leaders gain true wisdom, they can save their people.