Duke of Cleveland is a title that has been created twice, once in the Peerage of England and once in the Peerage of the United Kingdom. The dukedoms were named after Cleveland in northern England.
The first creation in 1670 (along with the barony of Nonsuch and the earldom of Southampton) was for Barbara Palmer, a mistress of King Charles II. The dukedom was created with a special remainder allowing it to be inherited by her first son, Charles FitzRoy, and his heirs male, then by her third son, George FitzRoy, 1st Duke of Northumberland, both being her illegitimate sons by Charles II. Charles FitzRoy was created Duke of Southampton, Earl of Chichester and Baron Newbury in 1675 and inherited the dukedom of Cleveland in 1709.
His son William inherited both dukedoms, but he had no issue, and since his uncle (Henry Fitzroy, 1st Duke of Grafton (died 1690), Barbara's 2nd son and his heirs male, had not been made eligible to inherit the peerage, the title became extinct upon his death.
The dukedom of Cleveland was created again in 1833 for William Vane, 3rd Earl of Darlington, along with the title Baron Raby. He was a great-grandson of Charles FitzRoy, the second Duke of the first creation, and had already been created Marquess of Cleveland in 1827. For more information on this creation, which became extinct in 1891, and the Vane family, see the Baron Barnard.