However, he was succeeded in the barony of 1665 according to the special remainder by his kinsman William Craven, the second Baron.

On his death, the title passed to his nephew, the sixth Baron, the son of Reverend John Craven.

His eldest son, the seventh Baron and first Earl, was a Major-General in the Army, and also served as Lord Lieutenant of Berkshire.

Also, Louisa, Countess of Craven (1785–1860), wife of the first Earl of the 1801 creation, was a well-known actress.

The current family seat is Hawkwood House near Waldron, East Sussex.

In Italy, in Varese, they lived at Villa Craven di Seyssel d'Aix starting from the mid-19th century.

Benjamin Robert Joseph Craven, 9th Earl of Craven (born 13 June 1989) is the only son of the 8th Earl and his wife Teresa Maria Bernadette Downes, a daughter of Arthur John Downes, of Black Hall, Clane, County Kildare, Ireland.

[4] The heir presumptive and the only person in the line of succession to the earldom, is the present holder's first cousin three times removed, Lt.-Cdr.