"It's a sled," Miller replied.note This is actually a doubleShout-Out - The term sled in racing circles is shortened from lead sled, which denotes a very fast vehicle. What was the Razorback? A racing star-ship.
Two characters make literary references, one to Moby-Dick and another to the "How can man die better" passage from the Horatius poem of Lays of Ancient Rome.
Holden initially wants to call the new Belter government the "Spacing Guild".
One of the ships of the "Free Navy" is called "Witch of Endor", the name of a character from The Bible.
Saba captains a ship named the Malaclypse, and at some point he refers to not liking to be "under the authority of the authorities". This will certainly be familiar to any reader of the Principia Discordia.
The pilot episode, "Dulcinea", and Holden's frigate Rocinante are named after Don Quixote's presumptive lover and horse, respectively. Holden's early exposure to Cervantes is explored in the (appropriately-titled) episode 'Windmills' when his mother Elise explains the Freudian Excuse behind his Chronic Hero Syndrome. Then there's the obvious parallels between Miller's obsession with Julie Mao and Don Quixote's obsession with Dulcinea.note The book also extends this to Holden, who gets a What the Hell, Hero? from Naomi because he can't distinguish love from desire, but the show hasn't gone into this.
"Rocinante" also works as a reference to both Alexis A. Gilliland's Rosinante trilogy, a book series similar to The Expanse, and the two-part song "Cygnus X-1" by Rush, in which the protagonist's spaceship is also called the Rocinante.
As shown here  the ship has three drones named "Peart", "Lee", and "Lifeson", which refer to Neil Peart, Geddy Lee, and Alex Lifeson of Rush.
Writer Mark Fergus explained at San Diego Comic-Con 2016 that Paj's severed arm spinning end over end in "Dulcinea" was intended to be a reference to the bone that does the same in 2001: A Space Odyssey, but admitted it was so abstract that almost nobody got it.
While Avasarala receives reports of the on-going attack on the Donnager, her husband Arjun can be seen and heard in the background reading Robert Louis Stevenson's Kidnapped to their grandson and his friends.
The design of Mateo's rock hauler from "Rock Bottom" was clearly inspired by the Starfuries from Babylon 5.
A public transit map of Ceres in "Dulcinea" includes a stop at "Cutty Station", named after Chad L. Coleman's (Fred Johnson) character "Cutty" Wise on The Wire.
A shop Miller visits in "Back to the Butcher" shares the name ("Tech Noir") of the bar in The Terminator.
When Bobbie kills Mao's henchmen with her power armor, she helps Chrisjen up in a recreation of the "Come with me if you want to live." shot. She then goes clearing out a way to their shuttle, telling he "I'll be right back."
The list of ships docked in "Salvage" has a lot of shout-outs, including the Serenity and the Burninator.
The scenes of Eros Station and its inhabitants being taken over by The Virus are straight out of Dead Space.
The protomolecule construct that eventually erupts from Venus looks an awful lot like a Brethren Moon.
The general design of the protomolecule-infected Eros Station is heavily reminiscent of the Upside-Down from Stranger Things.
Admiral Souther's ship, the Agatha King is named after two famous authors, Agatha Christie and Stephen King.
The protomolecule hybrid soldiers look very similar to the Husks from Mass Effect.
Speaking of Mass Effect, the psychic vision Holden gets from the Ring Station in "Dandelion Sky" is very reminiscent of the message that Shepard got from the Prothean beacon in the first game.
While at first glance the Ring's design is reminiscent of a lifeless Halo, Manéo Jung-Espinoza's attempt at flying through it reveals that it actually operates more like the Supergates built by the Ori.
One of the asteroids dropped by Marco is shown landing right on top of Dakar. This was the place Char planned to drop the Asteroid Axis in Mobile Suit Gundam: Char's Counterattack. Marco's uniform as leader of the Free Navy is also a blue version of Char's uniform in that movie.
Avasarala's contact list shown briefly in "Tribes" contains "Who, Dr.", "Stevens, D.", and "Clegane, G.", among others. All names of characters in shows that had been recast (like her husband's character had been).