What relevance does The Tempest have to our modern day life?
Well, there is a plot to get rid of Prospero and Miranda who end up lost and living on an island for several years because their little boat wrecked there. Shipwrecks happen often enough, and it is also repeated in movies and TV--Tom Hanks' movie Castaway where he is marooned on an island with only a volleyball for a companion and the TV show Lost are just two examples. I'm sure you can think of others...have you read The Lord of the Flies? That's another group left on an island to survive alone.
There is an ambitious brother who takes the title from his lost brother thinking he is dead. There are many such stories in history where brothers and sisters arrange for a usurption of power--especially where royalty is concerned--from other family members. Greed and ambition will always be relevant as long as there are human beings on this planet. Very rarely are people just satisfied with what they've got. They always want more.
There is also the couple who falls in love at first sight, and they end up getting married in the end--Ferdinand and Miranda make it a happy ending for everyone. Love is also a time-resistant theme, and it transcends all countries, social status, and culture.
There is much more to this play...disgruntled slaves, magical beings, supernatural events, drunken celebrations, mistaken identities...everything that people are still interested in and intrigued by in today's society.
I ask you, "How is The Tempest NOT relevant today?"