A manifold is said to have Ricci curvature lower bound in the spectral sense, if the first eigenvalue of the elliptic operator -γΔ+Ric is bounded below. This condition is usually strictly weaker than pointwise Ricci lower bound. This talk concerns the geometry of manifolds satisfying this condition. In particular, we will discuss the analogue of the classical theorems (Bonnet-Myers, volume comparison, Cheeger-Gromoll splitting) under our main condition. This talk is based on joint works with Gioacchino Antonelli and Marco Pozzetta.