Hamlet is a work of literature that was written roughly five centuries ago. Because of this, many of the ideas of the text might not feel relevant or even logical nowadays. However, many of them remain true to this day.
Some of the elements of the text that are still relevant are the feelings of revenge that Hamlet feels, as well as his inability to take quick action. Both of these are problems that modern readers can identify themselves with. Another element is the fact that Hamlet finds it very difficult to accept the idea of his mother remarrying. Finally, Claudius' ambition is also a topic that is relevant to the present.
On the other hand, the way in which Hamlet and Claudius struggle for the throne is less relevant nowadays, as most monarchies have now disappeared. Ophelia's lack of control over her own life is also a situation that has become much less common. Finally, the religious elements of the play are likely to be less powerful to a modern audience.