What relevance does the Iliad have today in modern times?
Now that is a good question. The Iliad is a classic and the reason it is so is because it is so applicable to all of us. The Iliad has many themes that are universal. Moreover, Homer is able to look at these themes in such great depth that it makes us think. Let me give you a few examples. The anger of Achilles is something that we can all relate to, because we all get angry at times. More importantly, what happens when groups or nations feel offended and their honor is hurt? There can be a war on account of great anger. Honor and anger are a few themes that the Iliad focuses on.
Another theme of the epic is war. This theme is always applicable. We are in war now and we probably will be for the rest of human existence. It has been that way and there is no indications of change.
Apart from the idea of themes, we can say that by studying the Iliad we learn a little more about ourselves. Why? Because the Iliad in many ways has shaped the Western way of thinking.