Bradbury uses a great many allusions in Fahrenheit 451.
Allusions allow the reader to learn about something they do not know about, by being reminded to something they do know about: taking previous knowledge, a comparison is made to bring that which is unfamiliar into focus. For example, if a kid is trying to describe to a friend how someone they know climbed a tree and was hanging from the top, he might say, "Mike was up at the very top, just like King Kong on the Empire State Building." If the friend has seen the movie or knows the story, the description is easier to imagine because he can recall images of King Kong fighting off the planes.
When Montag meets Clarisse, they connect in a way he does not understand. She sees the world the way it is rather than the way society expects her to see it. Montag notes at one point:
...what a shadow she threw on the wall!
One of Plato's works describes a dialogue between Plato's brother Glaucoma and Plato's mentor Socrates. The reference to the shadows refers to (for argument's sake) people who are chained to a wall in a cave and can never see anything but shadows thrown on that wall by a fire blazing behind them. They imagine they know what the shadows are, but...
According to Plato's Socrates, the shadows are as close as the prisoners get to viewing reality.
Clarisse has a clear vision of the world: she sees colors, the dew on the grass, and things Montag is not sure he has ever noticed. What Montag sees of life in his society is little more than a collection of images without clarity (like shadows) because he sees what society wants him to see, but Clarisse is in touch with reality. However, at this point Montag can only see the shadows.
The following may well be a Biblical allusion.
Shut up, thought Montag. Consider the lilies of the field.
The Bible verse alluded to is found in Matthew 6:28:
And why worry about your clothing? Look at the lilies of the field and how they grow. They don't work or make their clothing...
With the personification of the flowers, the reader is encouraged not to worry. The flowers in the field do not, yet they are cared and provided for.
The firemen are seen as agents of evil as they not only burn books, but people's homes as well. Note the description below:
Had he ever seen a fireman that didn’t have black hair, black brows, a fiery face…?
This might be an allusion to the devil, a being also associated with destruction and suffering by fire.
At the end of the book, there is an allusion to the famous mythical bird, the phoenix. Allegedly, the bird in five hundred year cycles would build a pyre and set himself ablaze, only to rise up again out of the ashes. The bird would do this repeatedly. When Montag travels through the woods with Granger, Granger alludes to the bird. When questioned, Granger describes the story of the bird and draws a comparison to what society does by destroying itself over and again. His hope is that someday mankind will stop in its continuous, self-destructive cycle:
...it looks like we're doing the same thing, over and over...We know the damn silly thing we just did...[maybe] someday we'll stop making the goddamn funeral pyres and jumping in the middle of them.
Allusions are effective only if the audience is familiar with the reference. An allusion to Gilligan's Island is meaningless if the audience doesn't know what it is.