England in the mid- to late-1400s
Richard III is set at the tail end of the English Wars of the Roses, which concluded with Richard's defeat and the establishment of the first Tudor monarch, Henry VII. From Richard's opening speech, we learn that Edward IV has just come to the throne again, which (from a historical standpoint) sets the year at 1471. The play ends with the Battle of Bosworth Field, which took place in 1485.
Yet, if interpreted tightly, the action of this Shakespeare play could occur over a mere 14 days. That means Shakespeare condensed the actions of about 14 years into less than a month. Obviously, he had to sacrifice a little historical accuracy. (Shakespeare never claimed to be a historian, or at least we hope he didn't, because he would he have been a bad one.)
This is why scholar G. Blakemore Evans referred to Shakespeare's flexibility with time as "telescoping." Basically Shakespeare tightly condenses the timing of the actual historical events, then mixes them around to suit his liking. He zooms us in to events he finds of interest and leaves out the more boring stuff.
The result is that the historical events are transformed into a narrative of tight pacing and lively action. Richard III is one of Shakespeare's longest plays but it doesn't feel that way because Richard is in a seriously big hurry to get his hands on the crown.
For being such a long play, Richard III is set in remarkably few places. For the first four acts, every scene (except one) is staged somewhere in London: anonymous streets, the palace rooms, the Tower of London, or at a handful of London houses. (The execution of Gray, Rivers, and Vaughn at Pomfret Castle in Act 3, Scene 3 is the only exception.) Only in Act 5, as the rival camps prepare for battle, do we get a refreshing scene change, passing through Salisbury and Tamworth before arriving at Bosworth Field for the final battle scene.
We might be tempted to think those Elizabethan acting companies were just being stingy with how many stage sets they had to create, but actually, the scene setting just might be significant. (After all, this is Shakespeare – everything is significant.) London was the seat of royal power in England, so it makes sense that this play about royal power would be anchored there. But then the departures from this pattern matter too.
Bear with us for a little bit here. The first four acts of the play occur while Richard is totally in control of his situation. Even for the period that he isn't king, Richard is carefully manipulating everything around him to lead to his coronation. Basically, while Richard is firmly in control of what's going on, the play focuses on the place where power is firmly stowed: London. Richard is entirely in control of himself and at home in the seat of royal politics; he's been able to hold the courtly world captive with his words and political maneuverings. That courtly world is symbolized by London, which is characterized by fear-stricken subjects and impressionable nobles.
However, as soon as Richard steps outside the safety zone of London's courtly world, his words can no longer protect him. He meets Richmond in hand-to-hand combat, and the two never speak a word to each other before Richmond just strikes him down.
Thus the few scene settings are arguably very deliberate. For the first four acts of the play, the world belongs to Richard; it's his to "bustle" in. The change of Act 5, Scene 1 isn't merely for pacing; it's a flashing neon sign. The stark change of location signals that the tides of the play have finally turned. Richmond comes from abroad; he's had nothing to do with the London court. His victory at Bosworth is a symbolic promise that the court of London is really about to change.