The subsidiary titles of the Duke of Wellington are: Marquess of Wellington (1812), Marquess Douro (1814), Earl of Mornington (1760 - but only inherited by the Dukes of Wellington in 1863), Earl of Wellington (1812), Viscount Wellesley (1760 - inherited in 1863), Viscount Wellington of Talavera and Wellington (1809), Baron Mornington (1746 - also inherited in 1863) and Baron Douro (1809). The Viscounty of Wellesley and the Barony and Earldom of Mornington are in the Peerage of Ireland; the remaining are in the Peerage of the United Kingdom.
Dukes of Wellington (1814)
The current heir to the title is the 8th Duke's son currently styled Arthur Charles Valerian Wellesley, Marquess of Douro. (He has chosen to use the style "Marquess of Douro", even though the peerage held by his father is "Marquess Douro".)