In one sense, one could say that the particular heroic culture in which the Iliad was embedded no longer actually exists. Warfare, for example, is not a matter of single combat between two males born into noble families according to a series of well-defined rituals, but instead involves extensive teamwork, planning, and technological expertise. Even actual combat in the sub-Mycenaean period was probably less ritualized and heroic than many books of the Iliad might have suggested; the introductory episode of the Greeks pillaging an innocent village and raping female teenagers is probably a realistic view of ancient warfare.
On the other hand, the myth of the "heroic code" still does influence our society. For example, from any practical viewpoint, going to war over a woman ditching her middle-aged husband for a handsome young man seems silly, as does the notion of throwing away hundreds of lives on the basis of wounded pride. Yet, in much of the rhetoric in the 2016 U.S. election campaign, and also in that espoused by many of the right-wing nationalist parties in Europe, one hears much of the same emphasis on tribalism and pride as opposed to a more modern pragmatism.
The issue of pride and petulance, especially as seen in Achilles' sulking over his honor to the point of subverting his own side in the war, has certain similarities to gang culture, in everything from its treatment of women simply as trophies to an exaggerated concern with status and image. As we look back at the Iliad, we can use it as a mirror to critique our own emphasis on pride and image and the way it stands in the way of sensible compromises and the ability to negotiate rather than resort to violence.