  In parallel with the evolution of femtosecond and attosecond laser as well as
free-electron laser technology, a variety of theoretical methods have been
developed to describe the behavior of atoms, molecules, clusters, and solids
under the action of those laser pulses. Here we review major ab initio
wave-function-based numerical approaches to simulate multielectron dynamics in
atoms and molecules driven by intense long-wavelength and/or ultrashort
short-wavelength laser pulses. Direct solution of the time-dependent
Schr\"odinger equation (TDSE), though its applicability is limited to He, ${\rm
H}_2$, and Li, can provide an exact description and has been greatly
contributing to the understanding of dynamical electron-electron correlation.
Multiconfiguration self-consistent-field (MCSCF) approach offers a flexible
framework from which a variety of methods can be derived to treat both atoms
and molecules, with possibility to systematically control the accuracy. The
equations of motion of configuration interaction coefficients and molecular
orbitals for general MCSCF ansatz have recently been derived. Time-dependent
extension of the $R$-matrix theory, originally develop for electron-atom
collision, can realistically and accurately describe laser-driven complex
multielectron atoms.
