The study of an almost Ricci soliton was introduced in a recent paper due to Pigola, Rigoli, Rimoldi and Setti. This structure represents a generalization to Einstein metrics and Ricci soliton, they appear as special solutions of the Ricci flow. In this seminar we shall talk about two results. The first treats of the characterization of compact almost Ricci solitons , more precisely, in this work we find some structure equations for almost Ricci solitons which generalize the equivalent for Ricci solitons. As a consequence of these equations we derive an integral formula for the compact case which enables to show that a compact nontrivial almost Ricci soliton is isometric to a sphere, provided either it has constant scalar curvature or its associated vector eld is conformal. Next, we prove that any compact almost Ricci soliton with constant scalar curvature is isometric to a Euclidean sphere. As a consequence we obtain that every compact almost Ricci soliton with constant scalar curvature is gradient.