I will describe a notion of a measured length space having a lower Ricci curvature bound. The definition is in terms of the transport of measures on the length space. The lower Ricci bounds are preserved under taking measured Gromov-Hausdorff limits. Various consequences are given, such as Bishop-Gromov inequalities, log Sobolev inequalities and Poincar´e inequalities. This is joint work with Cedric Villani