Differential Galois Theory, also known as Picard-Vessiot Theory, is the Galois Theory in the context of linear differential equations. This theory has been used fruitfully to establish Galoisian obstructions to integrability of hamiltonian and non-hamiltonian Systems as well to obtain integrability conditions of quantum integrable systems (relativistic and non relativistic Schrödinger equations, etc..).  In this talk, we present an overview of the results obtained by the speaker around these subjects. We present some motivating examples to convince graduate students and colleagues to participate in current projects such as applications of differential Galois theory to solve ordinary and partial differential equations.