We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of differential equations with respect to these parameters. We present the basic constructions and results, give examples, discuss how isomonodromic families fit into this theory and show how results from the theory of linear differential algebraic groups may be used to classify systems of second order linear differential equations. * This paper is an expanded version of a talk presented at the conference Singularités deséquations différentielles, systèmes intégrables et groupes quantiques, November 24-27, 2004, Strasbourg, France. The second author would like to thank the organizers of this conference for inviting him.