  Bound entanglement is a special form of quantum entanglement that cannot be
used for distillation, i.e., the local transformation of copies of arbitrarily
entangled states into a smaller number of approximately maximally entangled
states. Implying an inherent irreversibility of quantum resources, this
phenomenon highlights the gaps in our current theory of entanglement. This
review provides a comprehensive exploration of the key findings on bipartite
bound entanglement. We focus on systems of finite dimensions, an area of high
relevance for many quantum information processing tasks. We elucidate the
properties of bound entanglement and its interconnections with various facets
of quantum information theory and quantum information processing. The article
illuminates areas where our understanding of bound entangled states,
particularly their detection and characterization, is yet to be fully
developed. By highlighting the need for further research into this phenomenon
and underscoring relevant open questions, this article invites researchers to
unravel its relevance for our understanding of entanglement in Nature and how
this resource can most effectively be used for applications in quantum
technology.
