  A summary of recent researches on nuclear dynamics with realistic microscopic
quantum approaches is presented. The Balian-V\'en\'eroni variational principle
is used to derive the time-dependent Hartree-Fock (TDHF) equation describing
the dynamics at the mean-field level, as well as an extension including
small-amplitude quantum fluctuations which is equivalent to the time-dependent
random-phase approximation (TDRPA). Such formalisms as well as their practical
implementation in the nuclear physics framework with modern three-dimensional
codes are discussed. Recent applications to nuclear dynamics, from collective
vibrations to heavy-ion collisions are presented. A particular attention is
devoted to the interplay between collective motions and internal degrees of
freedom. For instance, the harmonic nature of collective vibrations is
questioned. Nuclei are also known to exhibit superfluidity due to pairing
residual interaction. Extensions of the theoretical approach to study such
pairing vibrations are now available. Large amplitude collective motions are
investigated in the framework of heavy-ion collisions leading, for instance, to
the formation of a compound system. How fusion is affected by the internal
structure of the collision partners, such as their deformation, is discussed.
Other mechanisms in competition with fusion, and responsible for the formation
of fragments which differ from the entrance channel (transfer reactions,
deep-inelastic collisions, and quasi-fission) are investigated. Finally,
studies of actinide collisions forming, during very short times of few
zeptoseconds, the heaviest nuclear systems available on Earth, are presented.
