The family were able to assert their influence within Gwynedd, their traditional sphere of influence, but by the 11th century they were ousted from Powys (Mid Wales) and Deheubarth (West Wales) by a series of strong rulers from the House of Dinefwr in Deheubarth, their dynastically junior cousins.
Members of the House of Aberffraw would include Idwal Foel, Iago ab Idwal, Cynan ab Iago, Gruffudd ap Cynan, Owain Gwynedd, Gwenllian ferch Gruffydd, Llywelyn the Great, Llywelyn ap Gruffudd, and Owain Lawgoch.