In what way is The Tempest related to modern time in our life?
When Shakespeare wrote The Tempest, he was inspired by news stories of the explorations undertaken by the British at the time, reports of the British discovering islands and continents they had not known existed. Today, the globe is well-charted, but the drive for adventure and exploration lives on in the probes we send out into space and deep into the bottom of the sea to gather information.
The political plot line of The Tempest in which Prospero uses his magic to seek revenge against those who dispossessed him and restore himself to his rightful power also remains relevant both on a large, world-political scale, in which power struggles between and within countries continue to play out, and on a smaller, interpersonal scale. We all occasionally feel power shifting within our social group dynamics and sometimes struggle to get that power back.
Finally, the story of first love between Miranda and Ferdinand remains timeless and universal. Miranda is essentially a school girl with a crush, newly aware of romance and sexuality because her life up until the start of the play has been so sheltered. This story of awakening attraction is one that has been told again and again, a thousand different ways, and will be told a thousand more.
A post-colonialist reading of The Tempest has been popular among scholars for a number of years. It has the advantage of contemporary relevance and can therefore tell us a great deal about modern life. On this reading, Prospero is presented as a proto-colonialist who's taken over a foreign island and proceeded to subject its indigenous population—in this case Caliban—to his unbending rule. Prospero is cruel to Caliban, treating him as little more than a slave. Caliban is encountered by his self-appointed lord and master as "The Other," a mysterious, barbarous creature who must be tamed and controlled.
This stands as a critique for how Westerners often perceive other cultures. Prospero gives Caliban the gift of language, in much the same way as the English language spread throughout the world on account of the British Empire. Yet Caliban's ability to speak the same language as Prospero simply serves to make it easier for him to understand and obey orders. As with colonialism and its modern-day cognate imperialism, paternalism and control often go together with Prospero.
The concept of revenge and retribution that occurs in The Tempest is also relevent to modern times. Prospero feels seriously wronged by Alonso and Antonio, so when he learns that Alonso's boat is near the island, he has Ariel create a storm to wash the boat onto the island. From there, he is able to turn the men's lives upside down in order to seek revenge for the wrong that was done to him in Milan.
Further, Caliban hates Prospero for having killed his mother Sycorax and then turning him into a personal slave on the island that is his rightful home. When Caliban meets Trinculo and Stephano, he feels that they have power and influence and makes a plan with them to overturn Prospero. Caliban wants revenge for the life of servitude that Prospero has made him suffer.
These ideas are still relevent in modern times as people seek revenge for wrongs that have been done to them.