  The detection and certification of entanglement and quantum correlations in
materials is of fundamental and far-reaching importance, and has seen
significant recent progress. It impacts both our understanding of the basic
science of quantum many-body phenomena as well as the identification of systems
suitable for novel technologies. Frameworks suitable to condensed matter that
connect measurements to entanglement and coherence have been developed in the
context of quantum information theory. These take the form of entanglement
witnesses and quantum correlation measures.
  The underlying theory of these quantities, their relation to condensed matter
experimental techniques, and their application to real materials are
comprehensively reviewed. In addition, their usage in e.g. protocols, the
relative advantages and disadvantages of witnesses and measures, and future
prospects in, e.g., correlated electrons, entanglement dynamics, and entangled
spectroscopic probes, are presented. Consideration is given to the
interdisciplinary nature of this emerging research and substantial ongoing
progress by providing an accessible and practical treatment from fundamentals
to application. Particular emphasis is placed on quantities accessible to
collective measurements, including by susceptibility and spectroscopic
techniques. This includes the magnetic susceptibility witness, one-tangle,
concurrence and two-tangle, two-site quantum discord, and quantum coherence
measures such as the quantum Fisher information.
