The nonbacktracking operator has been introduced in the 80's by Sunada and Hashimoto in the context of the Ihara zeta function on graphs. In 2013, Krzakala et al. have used this matrix for the design of an algorithm to detect communities in social networks. In recent years, this nonbacktracking matrix has been promoted as a powerful tool to analyse the interplay between geometry and spectrum of a graph. In this talk, we will introduce this matrix and give some recents results on the spectrum of random graphs or random matrices which rely on the use of the nonbacktracking matrix.