Superradiance and coherent atomic recoil lasing are two closely related phenomena, both resulting from the cooperative scattering of light by atoms. In ultracold atomic gases below the critical temperature for Bose-Einstein condensation these processes take place with the simultaneous amplification of the atomic matter waves. We explore these phenomena by surveying some of the experimental and theoretical developments that have emerged in this field of study since the first observation of superradiant scattering from a Bose-Einstein condensate in 1999 [1]. A 1D simulation of the dynamic, periodic spatial bunching of atoms into a density grating leading to the cooperative scattering of light into a mode backward propagating with respect to a pump laser field off-resonantly driving a two-level atomic transition. (a) A characteristic pulse of backscattered light is observed simultaneously with (b) the spatial bunching of atoms, as evident from the periodic convergence of the semiclassical trajectories of 500 atoms initially randomly distributed over an interval −10 < z < 10 in units of wavelength of the light