  We review some recent developments in nonperturbative studies of quantum
field theory (QFT) using the Schwinger-Dyson equations formulated directly in
Minkowski space. We begin with the introduction of essential ideas of the
integral representation in QFT and a discussion of renormalization in this
approach. The technique based on the integral representation of Green's
functions is exploited to solve Schwinger-Dyson equations in several quantum
field models, eg. in scalar models and in strong coupling $QED_{3+1}$ in the
quenched and in the unquenched approximation. The phenomenon of dynamical
chiral symmetry breaking in regularized theory is touched. In QCD, the
analyticity of gluon propagator on the complex momentum square plane is
exploited to continue some recent lattice data to timelike momentum axis. We
find non-positive absorptive part contribution in the Landau gauge gluon
propagator which is in agreement with some other new recent analyzes.
