In this very lyrical, poetic play, rich in imagery of water and musical sounds, Shakespeare engages with mystical themes and ideas taken from magic stories. Ariel is like a djinn from the 1001 Nights.
The text also engages with colonialism through the character of Caliban, who like Prospero has been disenfranchised. He is the original inhabitant of the island, demonised in his own description and through his mother, whose 'witch' status is devilish in contrast to Prospero's noble, white 'magician' role. This reflects the misogyny around the idea of sorcery. Caliban's behaviour is erratic and ambiguous. He has tried to rape Miranda and alternates between defiance and self-abasing deference, but his beautiful speeches indicate sensibilities that are not acknowledged by Prospero and Miranda, who see no injustice in his enslavement.
Miranda even has the gall to expect gratitude from Caliban because she has taught him their language. In this ignorance and in her passivity, she is on reflection an unsympathetic character, despite her obvious heroine role and her beauty.
The theme of colonial rule is also evident in the temptation the island exerts on everyone who comes to it to make himself king - comically so in the case of Stephano, whose clownishness perhaps underlines the foolishness and irrationality of the desire for power. The theme of master/servant is also reproduced time after time, as is the desire for liberation, through Ariel's bargaining with Prospero.
I saw a production of The Tempest at Shakespeare's Globe this week and had a bit of discussion about the problematic playing of Caliban in it (I read the play a few years ago)