Contents I. Introduction II. Quantum treatment of chemical dynamics - why and when? III. Quantum dynamical simulations of small systems IV. Methods for quantum dynamical simulations of large systems A. The Time-Dependent Self-Consistent Field (TDSCF) Method B. The Multiconfigurational and Configuration Interaction TDSCF C. The Classical Separable Potential method and its Configuration Interaction extension D. Gaussian-based semiclassical methods E. Dynamic path integral methods V. Applications A. Helium scattering from large argon and water clusters B. Spectroscopy and quantum dynamics of photoexcited pyrazine C. Electron photodetachment in the I$^-$Ar$_n$ (n=2-12) clusters D. Relaxation and Raman spectroscopy of photoexcited I$_2$ in rare gas environment E. Rotational control of HCl photodissociation in argon clusters F. Absorption lineshapes of electrons solvated in sodalites G. Hydrogen diffusion in crystalline silicon H. Retinal photoisomerization in bacteriorhodopsin VI. Summary and Conclusions VII. References