The Iliad, the Odyssey
It would be impossible to give a brief summary of the many, many, many (and also very complicated) ways in which the Aeneid alludes to Homer's Iliad and Odyssey. Not only is Virgil's whole poem an extended riff on these two poems, but it also refers to them constantly on the level of the individual word, line, and scene, sometimes borrowing in a straight-up way, sometimes playing around in a more tongue-in-cheek way. Finding Homeric references in the Aeneid is pretty much like a game of Where's Waldo – where Waldo is a line that DOESN'T come from Homer.
As one example of the subtle way in which Virgil uses this influence, let's take a look at the opening words of his poem: "Arms and the man I sing." Some people have interpreted this as a fancy way of saying "I sing of a man-at-arms," i.e., "I sing of a warrior." But doesn't that sound like kind of a funny way of saying that? Wherever something seems funny to you in Virgil (or, really, in any author), that should make you suspicious that something else is going on. In this case, it helps to know that the opening line of Homer's Iliad is "Sing, goddess, the anger of Peleus' son Achilleus," while the opening line of his Odyssey is "Tell me, Muse, of the man of many ways, who was driven." In the Greek (where you can put the words in just about any order you feel like), the first words of these respective lines are "anger" and "man." Now, the "anger" of Achilleus (the hero of the Iliad) happens in a military context, so that's pretty close to the "arms" (i.e., weapons) referred to in the first line of the Aeneid. It's not hard to see how the "man" at the beginning of the Odyssey matches up with…you guessed it, the "man" in the beginning of the Aeneid.
Coincidence? Well, it just so happens that the Aeneid is divided into two halves. Books 1-6 describe the wanderings of the hero, Aeneas; in this way, they match up with the Odyssey, which talks about the wanderings of its hero, Odysseus. Books 7-12 of the Aeneid describe warfare; in this way, they match up with the Iliad, which is all about warfare. So, basically, the first line of the Aeneid is Virgil's way of saying, "That's right, I'm going to be singing about a topic that includes BOTH the Iliad AND the Odyssey, except I'm going to put them in reverse order just to be tricky!" But wait – did he just say "I" am going to be singing? Doesn't that seem like a contrast with the more modest beginnings of the Homeric poems, where Homer asks the goddess to sing to him? Are you starting to get the picture?