The play Julius Caesaris a play for all times and therefore has as much modern significance as it did when William Shakespear wrote it 500 years ago.
One aspect that makes the play so successful is the dramatic irony Shakespear used to write it. In many instances in the play the audience knew what was going to happen, yet the actors did not. For instance, everyone knows that Brutus and the conspirators are going to kill Caesar since he died about 3000 years before the play was written.
Another aspect which made the play have modern significance was the use of the tragic hero. Both Brutus and Caesar had tragic flaws. Brutus's tragic flaw was his nobility which caused him to be easily manipulated by Cassius, and later kill Caesar. Caesar was a tragic hero. His tragic flaw was his power and that caused his downfall.
The play is also beneficial to the reader because it makes them aware of the powers of manipulation. Cassius completely turned Brutus away from his beloved friend Caesar. This shows the true powers that an evil and intelligent mind can have on another person.
Based on this and the pure language Shakespeare used in the play (like the speech on what a name really is), I believe that it will continue to have modern significance for years to come.