This is an introduction to the study of limiting spectra of sparse graphs. I first introduce the notion of local weak convergence, explain the crucial « convergence theorem » for the empirical spectral measure, and I detail the representation of the limiting measure. Then, I will explain the few results which are known on the asymptotic spectrum of Erdös-Rényi sparse graphs (and some extensions to other graphs models). Among those results are : the existence of a continuous part in the limit, the existence and location of atoms, the location of the atom at zero and the emergence of extended states at zero. I will finally mention several related questions.