  In the present note, a summary of selected aspects of time-dependent
mean-field theory is first recalled. This approach is optimized to describe
one-body degrees of freedom. A special focus is made on how this microscopic
theory can be reduced to a macroscopic dynamic for a selected set of collective
variables. Important physical phenomena like adiabaticity/diabaticity, one-body
dissipation or memory effect are discussed. Special aspects related to the use
of a time-dependent density functional instead of a time-dependent Hartree-Fock
theory based on a bare hamiltonian are underlined. The absence of proper
description of complex internal correlations however strongly impacts the
predictive power of mean-field. A brief overview of theories going beyond the
independent particles/quasi-particles theory is given. Then, a special
attention is paid for finite fermionic systems at low internal excitation. In
that case, quantum fluctuations in collective space that are poorly treated at
the mean-field level, are important. Several approaches going beyond
mean-field, that are anticipated to improve the description of quantum
fluctuations, are discussed: the Balian-V\'en\'eroni variational principle, the
Time-Dependent Random Phase Approximation and the recently proposed Stochastic
Mean-Field theory. Relations between these theories are underlined as well as
their advantages and shortcomings.
