  This Report explores recent advances in our understanding of the physics of
open quantum systems (OQSs) which consist of some localized region that is
coupled to an external environment. Examples of such systems may be found in
numerous areas of physics including mesoscopic physics that provides the main
focus of this review. We provide a detailed discussion of the behavior of OQSs
in terms of the projection-operator formalism, according to which the system
under study is considered to be comprised of a localized region ($Q$), embedded
into a well-defined environment ($P$) of scattering wavefunctions (with
$Q+P=1$). The $Q$ subspace must be treated using the concepts of non-Hermitian
physics, and of particular interest here is: the capacity of the environment to
mediate a coupling between the different states of $Q$; the role played by the
presence of exceptional points (EPs) in the spectra of OQSs; the influence of
EPs on the rigidity of the wavefunction phases, and; the ability of EPs to
initiate a dynamical phase transition (DPT). DPTs occur when the quantum
dynamics of the open system causes transitions between non-analytically
connected states, as a function of some external control parameter. In addition
to discussing experiments on mesoscopic quantum point contacts, we also review
manifestations of DPTs in mesoscopic devices and other systems. Other possible
manifestations of this phenomenon are presented. From these discussions a
generic picture of OQSs emerges in which the environmentally-mediated coupling
between different quantum states plays a critical role in governing the system
behavior.
