A review is presented of a new field in optical spectroscopy, in which the dynamics of wave packets composed of stationary states of atoms and molecules is studied. The time limits of applicability of the correspondence principle and wave packet collapse caused by nonlinear effects are considered. A new phenomenon is discussed, in which the wave packets are revived during their long-term post-classical evolution. Recent experiments on wave packet generation and detection in Rydberg atoms and molecules are reviewed. The experiments provide new opportunities for investigation of the transition region between classical and quantum physics of atomic particles. The relations between the phenomena discussed and the problem of generation of non-classical states of light in nonlinear optical systems is considered.