Quiver varieties have been invented by Nakajima to give a geometric construction of representations of quantum groups. They have also been used recently to construct monodial categorifications of cluster algebras. Quiver varieties associated with a quiver Q are defined by geometric invariant theory. In my talk, I will explain how they can be described explicitly as modules of certain mesh categories. We show that there is a bijection between their strata and the isomorphism classes of objects in the derived category of the quiver Q. We will also establish the link between quiver varieties and the desingularisation map defined in Giovanni Cerulli-Irelli's talk. This is joint work with Bernhard Keller.