  The study of the physical properties of open quantum systems is at the heart
of many present investigations which aim to describe their dynamical evolution,
on theoretical ground and through physical realizations. Here we develop a
presentation of different aspects which characterize these systems and confront
different physical situations which can be realized leading to systems which
experience Markovian, non-Markovian, divisible or non-divisible interactions
with the environments to which they are dynamically coupled. We aim to show how
different approaches describe the evolution of quantum systems subject to
different types of interactions with their environments.
