Title: Existence of zero-cycles on fibrations over number fields Abstract: For arbitrary smooth and proper varieties over a number field, Kato, Saito and Colliot-Thélène proposed, around 1990, precise conjectures on the existence of zero-cycles satisfying local conditions. Thanks to work of Saito, Salberger, Colliot-Thélène and Frossard, these conjectures are now known for fibrations, over curves with finite Tate-Shafarevich group, into Severi-Brauer varieties with squarefree index. In this talk I will present extensions of these results to more general fibrations.