  In a recent work [Phys. Rev. Lett. {\bf 98}, 140402 (2007)] we defined
``steering'', a type of quantum nonlocality that is logically distinct from
both nonseparability and Bell-nonlocality. In the bipartite setting, it hinges
on the question of whether Alice can affect Bob's state at a distance through
her choice of measurement. More precisely and operationally, it hinges on the
question of whether Alice, with classical communication, can convince Bob that
they share an entangled state, under the circumstances that Bob trusts nothing
that Alice says. We argue that if she can, then this demonstrates the nonlocal
effect first identified in the famous EPR paper [Phys. Rev. {\bf 47}, 777
(1935)] as a universal effect for pure entangled states. This ability of Alice
to remotely prepare Bob's state was subsequently called steering by
Schr\"odinger, whose terminology we adopt. The phenomenon of steering has been
largely overlooked, and prior to our work had not even been given a rigorous
definition that is applicable to mixed states as well as pure states. Armed
with our rigorous definition, we proved that steerable states are a strict
subset of the entangled states, and a strict superset of the states that can
exhibit Bell-nonlocality. In this work we expand on these results and provide
further examples of steerable states. We also elaborate on the connection with
the original EPR paradox.
