Image　quality　is　important　not　only　for　the　viewing　experience,　but　also　for　the　performance　of　image　processing　algorithms.　Image　quality　assessment　(IQA)　has　been　a　topic　of　intense　research　in　the　fields　of　image　processing　and　computer　vision.　In　this　paper,　we　first　analyze　the　factors　that　affect　two-dimensional　(2D)　and　three-dimensional　(3D)　image　quality,　and　then　provide　an　up-to-date　overview　on　IQA　for　each　main　factor.　The　main　factors　that　affect　2D　image　quality　are　fidelity　and　aesthetics.　Another　main　factor　that　affects　stereoscopic　3D　image　quality　is　visual　comfort.　We　also　describe　the　IQA　databases　and　give　the　experimental　results　on　representative　IQA　metrics.　Finally,　we　discuss　the　challenges　for　IQA,　including　the　influence　of　different　factors　on　each　other,　the　performance　of　IQA　metrics　in　real　applications,　and　the　combination　of　quality　assessment,　restoration,　and　enhancement.