I will report on our work, joint with Andreas-Stephan Elsenhans, on the Brauer-Manin obstruction for certain cubic and K3 surfaces. Concerning cubic surfaces, the talk will present the case of a 2-torsion Brauer class, explain how the corresponding surface arise, and show why they violate weak approximation. Concerning K3 surfaces, a particular type of Kummer surfaces is considered, for which the transcendental Brauer-Manin obstruction is particularly well understood.