How is the notion of real vs. unreal represented within The Tempest?

The real vs. the unreal is a major theme in William Shakespeare's play The Tempest. Prospero, the main character, is a powerful magician who uses his powers enact his revenge on his shipwrecked brother and his compatriots, bamboozling them with strange and terrifying visions. Due to Prospero's magic—who is aided by the spirit Ariel—the distinction between what is real and what is unreal is frequently blurred.
A rich textual example for the discussion of the relationship between the real and the unreal is in act 4, scene 1. In this scene, Prospero's daughter, Miranda, marries Ferdinand, and Prospero summons goddesses to celebrate their wedding. Once these visions disappear, Prospero delivers what is arguably the most famous speech in the play:

You do look, my son, in a moved sort,As if you were dismay'd: be cheerful, sir.Our revels now are ended. These our actors,As I foretold you, were all spirits andAre melted into air, into thin air:And, like the baseless fabric of this vision,The cloud-capp'd towers, the gorgeous palaces,The solemn temples, the great globe itself,Ye all which it inherit, shall dissolveAnd, like this insubstantial pageant faded,Leave not a rack behind. We are such stuffAs dreams are made on, and our little lifeIs rounded with a sleep. Sir, I am vex'd;Bear with my weakness; my, brain is troubled:Be not disturb'd with my infirmity:If you be pleased, retire into my cellAnd there repose: a turn or two I'll walk,To still my beating mind.

Here, Prospero reassures Ferdinand that what he has just seen was only a vision and, tellingly, compares this vision to the theater.
The Tempest is generally considered to be Shakespeare's farewell to theater; in this moving speech, Prospero—perhaps acting as a mouthpiece for his author—grapples with the fact that once the "visions" (invoked by the play) fade, nothing real is left behind.
Thus, The Tempest's relationship with the real and the unreal (or, in this case, the non-magical and the magical) is intimately tied to a meta-textual relationship between the "real" world and theater.