Sections of Families of Rationally Connected Varieties

In a paper from 2003, Graber, Harris, and Starr showed that over algebraically closed fields of characteristic zero, a morphism from a smooth projective variety to a smooth projective curve with rationally connected general fiber has a section. I will talk about their proof and some of the consequences, such as the way in which this is a generalization of Tsen's theorem. In particular, I will try to say something about the deformation-theoretic machinery that makes their constructions work.