Non-resonant inelastic X-ray scattering (NRIXS) is a new technique for atomic and molecular physics that allows one to measure the electronic structures and dynamic parameters of the ground and excited states of atoms and molecules in momentum space. There is a clearly understood physical picture of NRIXS, which reveals its remarkable advantages of satisfying the first Born approximation and being able to excite dipole-forbidden transitions. Various physical properties of atoms and molecules, such as their elastic and inelastic squared form factors, optical oscillator strengths, and Compton profiles, can be explored using NRIXS under different experimental conditions. In this paper, we review newly developed experimental methods for NRIXS, together with its characteristics and various applications, with emphasis on the new insights into excitation mechanism and other new information revealed by this technique. The intrinsic connections and differences between NRIXS and fast electron impact spectroscopy are elucidated. Future applications of this method to atomic and molecular physics are also described.