A God Am I: Greek Gods, of course - but they are just little-g gods. Later on Zeus goes on to delude himself into thinking he is the capital-G God, usurping Nix, the Fates, and possibly the actual capital-G God (referred to as the Quiet in-story). His comeuppance comes extremely swiftly at the hands of his son Achilles, leaving Hephaestus as the new lord of Olympos.
An Aesop: Several, one being "There has got to be more to life" along with the heavy Author Appeal of "Literature is amazing, and we should learn all we can from this people of the past" and "Everything happens for a reason."
Author Tract: The second half of Olympos is home to several dozen pages of the author expounding on how awesome writing is - fictional writing, non-fictional writing, etc. Taken as a whole with his comparisons of pre- and post-literate societies, can become somewhat Anvilicious after awhile.
Big Bad: Caliban for the Old-Style Human's story arc, the Gods of "Olympos" for the scholics trapped in the Iliad.
Bilingual Bonus: Savi mutters a phrase in Hebrew in the first novel that is not translated, thus causing readers to wonder what it is, although some can guess.
Bookworm: Harman, the only man on earth who knows how to read, and who admits to carrying around a bag of books. The scholics by default. Hell, they have the Iliad memorized and know what happens next as they watch it unfold before their eyes.
Brain Uploading: One of the defining attributes of the post-humans, who are described as "wearing" bodies. The so-called "old style" humans also use a variation of this - the million plus satellites in the rings around Earth are dedicated storage devices for their bodies and memories, and let them freely teleport all over the world when they feel like it.
The Casanova: Daeman believes himself to be this at the beginning of Illium.
Character Development: Daeman, Daeman, Daeman. Averted with almost all of the heroes inhabiting the ancient Greek setting.
Did Not Get the Girl: Daeman ends up with neither prominent female character (ie, Ada, Hannah), but he doesn't seem to mind. On the other hand, Hannah does not get the guy - she does not end up with Odysseus, however much she wants to.
Doorstopper: The novel clocks in at 573 pages, which is fair, as it is really two stories cut in half for readability. The continuation of the story happens in Olympos, and that companion novel takes the Doorstopper element of the books Up to Eleven - it clocks in at 690 pages.
Expy: Savi / Moira is essentially Rachel Wintraub of the Hyperion Cantos placed into a new setting. Much like Rachel, she can travel back and forth in time and her death brings rebirth for herself as "Moira" and the others of humankind. Heck, once Prospero even refers to her playfully as "Moneta", Rachel's nickname in the Cantos
It is explicitly stated that Moira is a post-human who took over Savi's appearance, and is not actually Savi.
Foreshadowing: Loads upon loads of it! Especially prominent in Ilium.
Genius Loci: The Earth's biosphere combines with the Internet to give rise to a basically sentient noosphere or something, which takes on the avatar of Ariel from Shakespeare's Tempest.
Greek Chorus: Invoked by Thomas at the very beginning of the, since he is supposed to be the Greek Chorus to the Gods who resurrected him. Played with, since the intro stylistically hews close to actual actual Greek Choruses ("Sing, O Muse..."), but then he actually lampshades the trope:
If I am to be the unwilling Chorus of this talk, then I can start the story anywhere I choose. I choose to start it here. [And the plot begins]
Jerkass: Daeman starts off like this, but thanks to Character Development, he grows out of it by the story's end. He's even happy for Ada and Harman, an attitude he would not have shown at the novel's beginning.
Loads and Loads of Characters: This is what happens when the entire cast of The Iliad, a resurrected Scholic, two sentient robot creatures, and a band of five old style humans on earth in one story. It's no wonder that the novels are huge.
Magic from Technology: The Olympian Gods, actually post-humans doing a little live-action role-playing, use technology that to all practical intents and purposes is magic.
Massive Multiplayer Crossover: Let's see...we have a re-enaction of the epic poem of Homer, two sci-fi robot creatures, and the people of an Earth that no longer remembers how to live (as they have essentially become Eloi) and the Reveal that another time traveller shares the same name as one from another continuity; the Hyperion Cantos. However, when you put the two together the facts match up: Moira is Jewish, as is Rachel, and they both are described as having dark hair and being able to travel through time, having a small romance of some sort. Put 'em all together and you get a work like this one.
To elaborate: Most of the major players from The Iliad show up, including Odysseus and Achilles. Characters from The Tempest appear, such as Prospero and Caliban. The Aeneid and the Posthomerica also get a few cameos.
No Bisexuals: Hockenberry almost blue screens when he sees Achilles and Patroclus snuggle up together after they have just had sex with women. Apparently he somehow missed the part about them being from Ancient Greece.
Parental Abandonment: Of a sort - none of the Old Style Humans living on Earth have any idea who their fathers are, though relationships with mothers remain important. Thus, when Harman tells Ada that he desires to stay alive beyond his "fifth twenty" (the maximum age a human is usually allowed to be, and also when most people choose to die) to be a father to their child, the idea is foreign and shocking to her, and she is actually angry at him for suggesting it at first.
The Plague: The Rubicon Virus, which was really a Synthetic Plague created by the Global Caliphate to kill the Jews, but which ended up spreading to most of humanity - ironically, the Jews were the only ones to survive it.
Precision F-Strike: Used occasionally as a means of showing how scared or nonplussed the characters are.
Really 700 Years Old: All of the old-style humans living on Earth. They can (and in most cases, do) live up to 100 years, all the while looking youthful.
Shout-Out: It's a Dan Simmons novel, who did you expect? A Moravec General in Olympos suggests nuking something from orbit, as it is the only way to be sure, along with other subtler shout outs to both modern pop culture.
The Singularity: The post-humans blew right through this centuries before the story begins. Subsequently feeling rather bored after unraveling the secrets of the universe they decide to go out and play god, Greek gods to be specific. It could also be said the other powerful forces at work in the story come through the singularity as well - writers of sufficient genius such as Homer and Shakespeare actually created or somehow glimpsed parallel universes in which their stories were true. This allows the post-humans to pull elements or entire planets from these other universes into our main one.
Teleporters and Transporters: The fax nodes used by the old-style humans, who later learn to "free-fax" to and from anywhere on Earth using direct access to the orbital systems that run the fax nodes. Post-humans had more powerful and self-contained quantum teleportation.
Time Travel: The French once developed a version that only allowed things to be sent into the future. The Global Caliphate of course tried to weaponize it. The post-humans have a more flexible kind, which allows travel into the past as well as alternate universes.
Tomboy and Girly Girl: Ada, who is demure, quiet, and in love with Harman, in contrast with Hannah, who makes her own furnace, wields Odysseus' sword, and in general is more of an Action Girl than Ada.
Transhuman: The post-humans/ Olympian Gods. Even so-called "old-style" humans have some shades of this, as implanted cybernetics give them access to "functions", most of which invoke networked technology to provide information and sensory enhancements, and as they later discover, the ability to teleport without having to use the fax nodes.
Unrealistic Black Hole: Really badly abused in one of the more ridiculous side plots in the novels. The Global Caliphate, having finally become so crazed as to want to destroy the world, somehow find the mass to create bowling ball sized black holes, then load them onto missiles somehow, and plan to launch them from a submarine. The plot fails of course. The bad science here is just so extreme that it breaks right through the boundaries that have already been pushed in the storyline.
Viewers Are Geniuses: One can only fully understand every reference after studying Homer's The Iliad, The Odyssey, and Shakespeare's The Tempest, Browning's 'Caliban upon Setebos' and also have some familiarity with The Time Machine, the complete works of Marcel Proust, Shakespeare's sonnets, and Hans Moravec's writings. They should know a decent amount about quantum physics, the Voynich manuscript, terraforming, transhumanism, and biosphere theory. Even then...no guarantees you'll get everything.
It helps that there are characters who love talking about Proust and The Iliad while much of the rest can be taken as "awesome magic stuff", but you won't really understand Noman-Odysseus's story arc at all unless you are up on a very large body of classical literature.