  We recall theoretical studies on transient transport through interacting
mesoscopic systems. It is shown that a generalized master equation (GME)
written and solved in terms of many-body states provides the suitable formal
framework to capture both the effects of the Coulomb interaction and
electron--photon coupling due to a surrounding single-mode cavity. We outline
the derivation of this equation within the Nakajima-Zwanzig formalism and point
out technical problems related to its numerical implementation for more
realistic systems which can neither be described by non-interacting two-level
models nor by a steady-state Markov-Lindblad equation. We first solve the GME
for a lattice model and discuss the dynamics of many-body states in a
two-dimensional nanowire, the dynamical onset of the current-current
correlations in electrostatically coupled parallel quantum dots and transient
thermoelectric properties. Secondly, we rely on a continuous model to get the
Rabi oscillations of the photocurrent through a double-dot etched in a nanowire
and embedded in a quantum cavity. A~many-body Markovian version of the GME for
cavity-coupled systems is also presented.
