  This short article concentrates on the conceptual aspects of the violation of
Bell inequalities, and acts as a map to the 265 cited references. The article
outlines (a) relevant characteristics of quantum mechanics, such as statistical
balance and entanglement, (b) the thinking that led to the derivation of the
original Bell inequality, and (c) the range of claimed implications, including
realism, locality and others which attract less attention. The main conclusion
is that violation of Bell inequalities appears to have some implications for
the nature of physical reality, but that none of these are definite. The
violations constrain possible prequantum (underlying) theories, but do not rule
out the possibility that such theories might reconcile at least one
understanding of locality and realism to quantum mechanical predictions.
Violation might reflect, at least partly, failure to acknowledge the
contextuality of quantum mechanics, or that data from different probability
spaces have been inappropriately combined. Many claims that there are definite
implications reflect one or more of (i) imprecise non-mathematical language,
(ii) assumptions inappropriate in quantum mechanics, (iii) inadequate treatment
of measurement statistics and (iv) underlying philosophical assumptions.
