  This review focuses on the field of quantum entanglement applied to condensed
matter physics systems with strong correlations, a domain which has rapidly
grown over the last decade. By tracing out part of the degrees of freedom of
correlated quantum systems, useful and non-trivial informations can be obtained
through the study of the reduced density matrix, whose eigenvalue spectrum (the
entanglement spectrum) and the associated R\'enyi entropies are now well
recognized to contains key features. In particular, the celebrated area law for
the entanglement entropy of ground-states will be discussed from the
perspective of its subleading corrections which encode universal details of
various quantum states of matter, e.g. symmetry breaking states or topological
order. Going beyond entropies, the study of the low-lying part of the
entanglement spectrum also allows to diagnose topological properties or give a
direct access to the excitation spectrum of the edges, and may also raise
significant questions about the underlying entanglement Hamiltonian. All these
powerful tools can be further applied to shed some light on disordered quantum
systems where impurity/disorder can conspire with quantum fluctuations to
induce non-trivial effects. Disordered quantum spin systems, the Kondo effect,
or the many-body localization problem, which have all been successfully
(re)visited through the prism of quantum entanglement, will be discussed in
details. Finally, the issue of experimental access to entanglement measurement
will be addressed, together with its most recent developments.
