We present new methods for time-dependent quantum mechanical simulations of large
polyatomic systems and their applications to photochemical processes in clusters.
Two related approaches are discussed: 
The Classical Separable Potential (CSP) approach, and its
extension towards Configuration Interaction (CI-CSP). The former scheme assumes
separability of the vibrational modes of the system, and describes each mode as
moving in a mean field due to the other modes. The basic idea, which
allows for quantum simulations of hitherto unaccesibly large systems, is that 
the effective single-mode potentials are
obtained from a classical MD simulation that precedes the quantum calculation.
The second approach represents an improvement that corrects for correlations
between different modes, resulting in a scheme of good accuracy. 
Applications of the methods are presented for
dynamics following photodetachment in a small I-(Ar)2 cluster (where
comparison with numerically exact calculation is possible) and for
photoexcitation dynamics and spectroscopy of atomic and molecular impurities in
large clusters, such as I2(Ar)17 and I2(Ar)47.
Future directions of method development 
are suggested in the light of the algorithmic
aspects and the applications.