The concept of L-orthogonality has been the focus of research in the past decades, partly due to its connection with the presence of copies of l_1. In recent years this line of research has found connections with research in set theory, through the use of special ultrafilters; mainly Q-points. In this talk we will present the concept of Q-measures, a generalization of Q-points, its connection with the research in L-orthogonality and some consistency and independence results. This is joint work with Antonio Avilés, Gonzalo Martínez Cervantes, and Alejando Poveda.