We can learn an awful lot about social structures and how the different genders were expected to behave.

In the Iliad and Odyssey we can clearly see how the search for kleos affected males, how women were clearly thought of as secondary citizens (Penelope has next to no power when Odysseus isn't about even though she is technically the queen, Helen was repeatedly demonised), and Xenial traditions also come across clearly. This last point is seen often in the Odyssey, and again in the Iliad where two of the competing soldiers trace back their history generations and decide to not fight each other, but exchange gifts and their very armour.

In the Aenied a similar treatment of women is shown (even the gods and goddesses here are much more deceitful and portray how females are weaker/worse than their male counterparts), and the idea of piety screams at us at every avenue. The story is often dismissed as just being propaganda for the emperor, but the main focus is the shift from barbaric furor etc, to a newer, supposedly better and more sophisticated social hero. The conclusion of this epic, however, indicates that nobody can ever rid themselves of uncontrollable fury, and begs the question; should we want to?

If anybody wants any more info or examples I'll reply as I know I have made a few sweeping statements or presumptions here but they were just the briefest of examples/explanations