  Entanglement plays a pervasive role nowadays throughout quantum information
science, and at the same time provides a bridging notion between quantum
information science and fields as diverse as condensed-matter theory, quantum
gravity, and quantum foundations. In recent years, a notion of ''Generalized
Entanglement'' (GE) has emerged, based on the idea that entanglement may be
directly defined through expectation values of preferred observables -- without
reference to a preferred subsystem decomposition. Preferred observables capture
the physically relevant point of view, as defined by dynamical, operational, or
fundamental constraints. While reducing to the standard entanglement notion
when preferred observables are restricted to arbitrary local observables acting
on individual subsystems, GE substantially expands subsystem-based entanglement
theories, in terms of both conceptual foundations and range of applicability.
Remarkably, the GE framework allows for non-trivial entanglement to exist
within a single, indecomposable quantum system, demands in general a
distinction between quantum separability and absence of entanglement, and
naturally extends to situations where existing approaches may not be directly
useful -- such as entanglement in arbitrary convex-cones settings and
entanglement for indistinguishable quantum particles. In this paper, we revisit
the main motivations leading to GE, and summarize the accomplishments and
prospects of the GE program to date, with an eye toward conceptual developments
and implications. In particular, we explain how the GE approach both shares
strong points of contact with abstract operational quantum theories and,
ultimately, calls for an observer-dependent redefinition of concepts like
locality, completeness, and reality in quantum theory.
