Shakespeare is thought of as the most famous of the Elizabethan playwrights. But he actually did a large amount of his work in the Jacobean era, and he gained serious recognition only after Elizabeth left office. In fact, the succession of James 1 from Elizabeth 1 in 1603 is seen as a watershed moment in Shakespeares career. Popular tastes changed, with a taste for satire and tragicomedy coinciding with the accession of the new king. Though he wrote a lot of works under Elizabeth, plays such as Othello, King Lear, and Macbeth were written under James I, and influenced by the new king. Macbeth was even written to gain the James respect by confirming his legitimacy. Its not easy to classify a playwright like Shakespeare who straddled two clearly opposed periods. But his later plays were definitely not Elizabethan.
