In this talk I will present the basic ideas of the D(iscontinuous)-P(etrov)-G(alerkin) method with optimal test functions which was introduced by Demkowicz and Gopalakrishnan in 2009. We will have a look at the abstract theory and in particular at the concept of optimal test functions. Then, I will define an ultraweak formulation of Poisson's equation and explain how to apply the abstract ideas of DPG methods to this particular case. Finally, I will discuss several problems where the DPG method has been used successfully. These applications range from singular perturbation problems to plate bending problems.