In this seminar we present the stress-energy tensor as the fundamental object in the study of a quantum field theory on a curved background. We discuss its convenience with respect the somehow misleading concept of particles, and also the consequences from the implicit gravitational interaction, such as additional divergences even for free fields. These ones suggest the development of new different renormalization techniques in curved space-time, rather than the usual normal-ordering employed in Minkowski. In this talk we will focus mainly on the so called adiabatic scheme, and compare it to the DeWitt-Schwinger formalism. Some new features from the renormalization theory will be derived (conformal anomalies), and some applications in cosmology will be presented to show the power of this method.