Methods for time-dependent quantum-mechanical simulations of large polyatomic
systems are described and analyzed, and applications to processes in clusters
are presented. Two basic methods are discussed: (i) The Time-Dependent
Self-Consistent Field (TDSCF) approximation and its generalizations;
(ii) The Classically-Based Separable Potential (CSP) approach, and its
extensions. At their simplest respective levels, both methods assume
separability of the different modes of the system, and describe each mode as
moving in a mean field due to the other modes. In TDSCF the effective 
single-mode potentials are computed quantum-mechanically, in CSP they are
obtained from a classical MD simulation that precedes the quantum calculation.
For both methods, improvements are available that correct for correlations
between different modes, resulting in approaches of good accuracy. Both the
TDSCF and the CSP approach make possible calculations for systems of size and
complexity that could hitherto not be treated. Algorithmic and computational
aspects of the two methods are examined, and it is found that in typical
molecular applications the methods are nearly identical in accuracy, but CSP is
greatly superior computationally, especially in applicability to much larger
systems than TDSCF. Applications of the methods are presented for: (1)
Photoexcitation dynamics and spectroscopy of atomic and molecular impurities in
large clusters, e.g., for I2(Ar)n. (2) Collision dynamics, energy
transfer and state-to-state transitions in atom-cluster scattering, e.g.,
He + (Ar)n , Ar + (H2O)n.
Future research directions are suggested in the light of the algorithmic
aspects and the applications.