Richard III is a play about violence, concluding a long cycle of violence that Shakespeare began in Henry VI part 1. The War of the Roses has taken Richard's father, Richard Duke of York, and his brother Edmund, Earl of Rutland. The families have been at war for decades. Assassination is the expected route to the throne.
Into this world steps Richard. His harsh and difficult birth left his mother ruined and unable to love the crippled, ugly thing she had brought into the world. Unloved by his mother and believing no woman would ever love him, he has decided to play by the rules that the world has set up for him. He will receive his power through violence and deception. Richard has been raised to kill, and it is the best tool he knows.
If murder is the way to the most respected office in the land, he will murder. If possession of a woman will give him claim to that throne, he will seduce her, despite his own shortcomings. In fact, he will use them to his advantage: he manipulates Anne through her pity for his wretched state.
If his brothers stand between him and the throne, what binds him to them to prevent him from murdering them, if he can get away with it? Or with murdering children? It is all one and the same to him, and that's his ultimate downfall.
Everybody remembers the Princes in the Tower. It is the trait for which he is known best, after being a hunchback. It seems to mark the turning point in the play, where Richard gradually loses his ability to control. Buckingham is horrified at the murder, even though he is complicit in the deaths of nearly a dozen adults over the course of the play. It is the point in the play at which Richard's masterful control begins to slip, his supporters turn away from him, and he spirals quickly into destruction.
In the end, the York family turns even on itself, destroying every last member until the last dying member of the Lancaster family, Margaret, throws the last bomb, backing Henry Tudor to ultimately supplant the Plantagenet reign of England that had lasted for over three hundred years. A final murder brings to an end one English dynasty, and begins another.
The historical figure of Richard, Duke of Gloucester, is very different from the figure presented in Shakespeare's play. There is good reason to believe that Richard did not murder the young princes, and some writers have even suggested that they were murdered instead by Henry Tudor himself, grandfather of Queen Elizabeth.
The play is sometimes tweaked to make Richard less complicit in the murders, to resurrect an image of Richard that was created by Tudor historians to cement Henry's (somewhat dubious) claim to the throne. I treat this play instead as a piece of fiction. Richard was not a hunchback, but I accept Shakespeare's contention that he was. I accept Shakespeare's contention that Richard was responsible for nearly a dozen murders in the course of the play.
In all that violence, I find a kind of karmic retribution, perhaps the truest kind of revenge. There is hardly a figure in the play who has not profited by violence. Elizabeth is now queen of England for the murder of Henry. Edward achieved his throne the same way. Clarence uses murder to repent for his betrayal. Margaret kept her throne for as long as she did by murdering Richard's father and brother. The Yorkist supporters have earned peerages. All accept the contention that violence is the way things are done. None has stepped up to condemn any murder except to swear revenge.