  We offer a systematic account of decomposition of quantum systems into parts.
Different decompositions (structures) are mutually linked via the proper linear
canonical transformations. Different kinds of structures, as well as their
relations, are considered. Emphasis is placed on mutually global and
irreducible structures. Is there a privileged structure of the closed system?
Is there a preferred (bipartite) structure of an open system? Are there any
practical advantages of certain alternative structures of the system? Is there
a simple dynamical relation for a pair of structures? The [necessarily partial]
answers are rather intriguing. Relativity of quantum correlations (that include
entanglement as well as the "one-way" and "two-way" discord) is carefully
presented. Emphasis is placed on the "parallel occurrence of decoherence" in
the quantum Brownian motion. The environment-selected preferred structure of an
open composite system is presented for a pair of harmonic oscillators (or the
field modes). A limitation of the Nakajima-Zwanzig projection method appears as
a consequence of quantum correlations relativity. Hence, describing dynamics of
an alternate open-system is a delicate task. Certain interpretational issues,
which include "quantum reference frames" issue, are discussed. Some recent
experiments are also discussed. To this end, the option that "there are no
particles" on the most fundamental physical level naturally follows. Certain
open questions and prospects for further research are highlighted.
