In this seminar we discuss about isoperimetric inequalities and Gamma-convergence of fractional perimeters in the Gaussian setting. To give a notion of fractional perimeter and to face these problems we use, as in the Euclidean case, both an extension method and an approach based on a set-functional depending on a fractional singular kernel. These results were obtained in collaboration with S. Cito, D. A. La Manna and D. Pallara.