Appears in collection : Summer School 2015: Moduli Problems in Symplectic Geometry

We will explain the relevance of Lagrangian cobordisms in Lefschetz fibrations to the study of the (derived) Fukaya category of the fiber. In particular we will give a cobordism interpretation of Seidel's long exact sequence, introduce cobordism groups and also outline how to study real algebraic structures using cobordisms. The talk is based on joint work with Octav Cornea.