The theory for ultrafast X-ray and electron scattering is presented in a unified form, derived using time-dependent perturbation theory, and applied specifically to molecules in the gas phase. The components of the scattering signal (elastic, inelastic, and coherent mixed) are identified and their physical origins are discussed. A brief overview of the calculation of scattering matrix elements, which are required for both analyses and simulations of scattering experiments, is given. Finally, a framework that accounts for rotational averaging as well as alignment due to single-photon excitation in the weak-field limit is provided.