As with many of Shaw's plays, the main theme of Caesar and Cleopatra is war and politics. While other writers might have thought of the relationship between the Egyptian queen and Roman political leader in terms of a romance, Shaw suggests that a sophisticated, middle-aged Roman such as Caesar would actually have little romantic interest in a child he would have seen as superstitious, naive, and barbaric, but instead, as a fundamentally decent man, might have acted as a mentor to the young Queen.
In the play, Cleopatra, although still a child, is primarily concerned with establishing exclusive rulership over her kingdom, rather than joint rulership with her brother. Caesar is engaged in a war against Pompey, a fellow Roman with whom, in the past, he jointly ruled Rome as part of a triumvirate. Both characters, therefore, are in similar situations.
Caesar, though, unlike the Egyptians, objects to unnecessary violence, and much of the play consists of tension between Cleopatra's superstitious beliefs and willingness to conduct assassinations, and Caesar's rational pragmatism, which sees fairness as legitimating power. Thus a central theme is what makes authority legitimate.
One theme some scholars and readers have suggested is that of politics. The game of politics is what may have brought these two leaders together. Caesar could have been drawn initially to Cleopatra by her beauty but ultimately remained by her side because of the monetary and agricultural wealth of Egypt. Cleopatra may have been in love but needed a powerful ally that would enable her to reign in Egypt as sole ruler without the additional influence of her siblings. The Roman Empire would make for a formidable ally should Egypt come under attack from an outside force greater than what Egypt had available at that point in history.