  The distribution of quantum states over long distances is limited by photon
loss. Straightforward amplification as in classical telecommunications is not
an option in quantum communication because of the no-cloning theorem. This
problem could be overcome by implementing quantum repeater protocols, which
create long-distance entanglement from shorter-distance entanglement via
entanglement swapping. Such protocols require the capacity to create
entanglement in a heralded fashion, to store it in quantum memories, and to
swap it. One attractive general strategy for realizing quantum repeaters is
based on the use of atomic ensembles as quantum memories, in combination with
linear optical techniques and photon counting to perform all required
operations. Here we review the theoretical and experimental status quo of this
very active field. We compare the potential of different approaches
quantitatively, with a focus on the most immediate goal of outperforming the
direct transmission of photons.
