Shakespeare's play Antony and Cleopatra revolves around these actual characters from Roman and Egyptian history. This is the second of Shakespeare's trilogy of Roman plays—the first was Julius Caesar, better received at the time than Antony and Cleopatra was during the bard's lifetime. (The third play is Coriolanus.)
This story is a continuation of that which began in Julius Caesar. When Caesar is murdered by Brutus, Cassius and other co-conspirators, a second triumvirate is formed. A triumvirate is
...a government of three officers or magistrates functioning jointly
This group included Octavius (Caesar's adopted son and heir), Antony (who deeply loved Caesar), and Lepidus, an older and accomplished former soldier who Antony—with Octavius' begrudging agreement—delegates to a lesser role. Brutus and his murderous compatriots are defeated, and Antony takes a leading role in governing Rome.
In Antony and Cleopatra, Antony goes to Egypt, where he falls in love with Egypt's queen, Cleopatra. Because the action of the play moves back and forth between Antony's home and scenes with Cleopatra, the setting of the play is Rome, Egypt and several battlefields—the battlefields become a part of the play as Octavius eventually accuses Lepidus of treason, and attacks and defeats Antony's troops in Egypt.
Antony, wrongfully believing Cleopatra is dead, tries to kill himself, and—wounded, is taken to the queen. When Antony dies, Cleopatra and two of her servants commit suicide. Octavius orders a "state funeral" for the lovers, and departs for Italy, the sole ruler of Rome.