  This paper reviews the progress that has been made in our knowledge of
quantum correlations at the mesoscopic and macroscopic level. We begin by
summarizing the Einstein-Podolsky-Rosen (EPR) argument and the Bell
correlations that cannot be explained by local hidden variable theories. It was
originally an open question as to whether (and how) such quantum correlations
could occur on a macroscopic scale, since this would seem to counter the
correspondence principle. The purpose of this review is to examine how this
question has been answered over the decades since the original papers of EPR
and Bell. We first review work relating to higher spin measurements which
revealed that macroscopic quantum states could exhibit Bell correlations. This
covers higher dimensional, multi-particle and continuous-variable EPR and Bell
states where measurements on a single system give a spectrum of outcomes, and
also multipartite states where measurements are made at multiple separated
sites. It appeared that the macroscopic quantum observations were for an
increasingly limited span of measurement settings and required a fine
resolution of outcomes. Motivated by this, we next review correlations for
macroscopic superposition states, and examine predictions for the violation of
Leggett-Garg inequalities for dynamical quantum systems. These results reveal
Bell correlations for coarse-grained measurements which need only distinguish
between macroscopically distinct states, thus bringing into question the
validity of certain forms of macroscopic realism. Finally, we review progress
for massive systems, including Bose-Einstein condensates and optomechanical
oscillators, where EPR-type correlations have been observed between massive
systems. Experiments are summarized, which support the predictions of quantum
mechanics in mesoscopic regimes.
