Most of the Odyssey is spent describing events which could not possibly have happened in our non-mythic consciousness understanding of the world. The Odyssey is a little more up in the air. There is barely enough to conclude that a real people were described.

However, there isn't enough evidence to draw the conclusion that the Trojan War happened as described in our transcription of events. Additionally, it seems that helmets described in the Iliad were in use at the time.

'The Trojans and Their Neighbors' delves into this topic further, drawing parallels between story elements that appeared in the Iliad and descriptions of peoples and cultures that appeared in the area. It likely corresponds to modern-day Hisarlik. The city of Troy did exist, and the geography described matches the region. However, it does appear to have alluded to some real events and places, which means that it might actually have a historical basis. In the case of the Iliad, the story as written is removed from its transcription by roughly four centuries. Remember that these are oral traditions just because they once told stories that happened doesn't necessarily mean they still do. Note, though, that it implies that you have to take any historical basis with a grain of salt. So, I'm going to go out on a limb and rephrase your question for you: did The Iliad and The Odyssey develop around historical events? This question is actually more directly answerable. These stories get told and re-told they accrue variations, adopt easily memorizable rhythms, and underwent significant changes as time went on. Stories like these may have traced real events, but they were educational tools about good manners, how to treat guests, marks of cultural significance, and just generally how the gods affect peoples' lives. They didn't arise from Greek mythology (any more than mythology arises from itself), because in oral tradition mythology, story and history quickly blend together. So, the major correction to your question is: The Iliad and The Odyssey are a part of Greek mythology. It's even debatable whether anyone named 'Homer' even existed at all, but if they did, certainly all they did was transcribe a purely verbal story that was passed down for generations. The Iliad and The Odyssey aren't texts written by Homer. I'm going to start with a minor framing correction, before I go on to actually answer your question.

The story of iliad and odyssey