Shakespeare's English history plays were based on a variety of historical sources, so he made /some/ attempt at having /some details/ correct, but he certainly also embellished some facts and highly simplified or deleted other facts to increase drama and simplify plot. His sources themselves were often very biased toward a version of history that supported Tudor legitimacy (although I'm unclear on whether that bias was widely known in Shakespeare's time or not). He also definitely shaded some facts and characters one way or another in order to keep the political leaders and censors of his time happy.

Shakespeare's Sources -

Basically every English history play - Holinshed's Chronicles of England, Scotland, and Ireland (1587 - 2nd edition) - This was a highly dramatized version of English history that is apparently just really inaccurate in a lot of places. I really need to read it someday. [also a source for Macbeth and King Lear]

Richard III - Thomas More's History of King Richard the Thirde (1513) - More's portrayal of Richard III as deformed, to the point of causing his mother a particularly troublesome birth, is probably the most famous bit that Shakespeare took from that source. In actuality, though Richard III's skeleton showed that though he had significant scoliosis and likely had visibly uneven shoulders, he wouldn't have had a hunchback.

Simplification -

Shakespeare HIGHLY simplified a lot of the events of the Wars of the Roses in his Henry VI Parts II and III. And honestly....you can't really blame him. I made a simplified timeline of the main events of the Wars of the Roses in November and it's still incredibly complicated (and honestly, it took forever). You can see it on my blog here - https://www.rachaeldickzen.com/blog/2019/11/11/the-wars-of-the-roses-a-timeline-of-main-events

Examples:

- In Henry VI Part 3, as soon as the Earl of Warwick discovers that his protege Edward IV had secretly married Lady Grey (Elizabeth Woodville) while Warwick is off trying to organize a French alliance and marriage for Edward IV, he joins forces with Margaret of Anjou, marries his daughter Anne to her son Edward, and frees Henry VII. This all happens in the space of two acts.

IN ACTUALITY, Edward married Elizabeth Woodville in 1464, but Warwick didn't rebel against Edward IV until April 1469 (rebellion #1). He joined forces with Edward's brother George, Duke of Clarence, and actually captured Edward IV, but eventually released him when it became clear that Parliament wouldn't cooperate with his plan to rule the country through Edward. He and George/Clarence rebelled AGAIN in July 1470 (rebellion #2), but this one didn’t go so well and their plan quickly falls apart. Warwick flees to France, plots with Margaret of Anjou (rebellion #3), marries his daughter to her son Edward, and goes back to England in October 1470 to put Henry VI back on the throne.

I mean. It's easy to understand why Shakespeare cut out a few rebellions there, just for the sake of time and to keep things from being super confusing.

- Richard III portrays Richard marrying Anne Neville immediately before the death of his brother Edward IV and becoming king not too long after. In actuality, Richard and Anne married in spring 1472, Edward IV didn't die until April 1483, and Richard III didn't become king until July 1483.

Dramatic alterations -

Various examples:

- Henry IV Part 1 - Sir Henry Percy (Hotspur) is portrayed as a young man the same age as Prince Hal, but in reality, Hotspur was actually three years older than Hal's dad Henry IV. This increases drama by placing pressure on Hal to behave more like the ambitious leader Hotspur.

- Henry V - In the play, it's stated that the English had fewer than 30 casualities while the French had 10,000! In actuality, about 112-600 of the English and about 6,000 of the French were killed.

- Henry VI Part 1 - The famed "roses" of the Wars of the Roses are a bit of a Tudor invention, which Shakespeare expanded on. Although the Yorks did use the white rose as a symbol from early on in the conflict, the Lancastrian red rose wasn't used until after Henry Tudor defeated Richard III at the Battle of Bosworth. These two roses were combined to form the "Tudor Rose," a symbol of the unity of the two houses.

In addition, it also just isn't accurate to imagine that only one symbol was used by each noble family. Just among the York brothers alone, in addition to the white rose, Edward IV used the sun in splendor, a falcon, a black dragon, and a white lion (among several others), while Richard used a white boar and "a white falcon with a virgin's face holding a white rose." But again, portraying that in a play would make things very confusing (and Shakespeare’s histories are already confusing enough when it comes to names, since he often refers to characters by their titles, which often change!).

- Henry VI Part 2 - Richard of Gloucester (the eventual Richard III), and his brother Edward (eventual Edward IV) are both portrayed as adults at the time of the first battle of St. Albans. Historically, Richard was only 3 years old and Edward was only 13 when this battle occurred.

- In addition, a TON of the events in Richard III are inserted for dramatic effect. There is zero evidence that Richard killed his wife Anne (she probably died of tuberculosis), and he definitely didn't seduce her at the funeral for her father-in-law Henry VI. Henry VI died in May 1471 and Anne and Richard didn't marry until the spring of 1472. There's also good evidence that Richard and Anne actually really had a lovely romance; he was determined to marry her and may have rescued her from his brother Clarence's attempts to hide her away. Anne and Richard were crowned in the first joint coronation in almost 200 years. But this doesn’t suit the Tudor propaganda need to portray Richard as a villain.

George Duke of Clarence is portrayed very sympathetically in Richard III, but in reality, he was kind of a jerk who rebelled against his own brother 2-3 times and continually tried to start up trouble. The play also shows Clarence being murdered by Richard's (hilarious) henchmen, but in actuality, Clarence was put on trial for treason, and privately executed on the order of his brother Edward IV.

The disappearance of the Princes in the Tower was blamed on Richard III at the time, but there's no actual evidence connecting him (or really anyone) to their deaths.