  We formally link the concept of steering (a concept created by Schrodinger
but only recently formalised by Wiseman, Jones and Doherty [Phys. Rev. Lett.
98, 140402 (2007)] and the criteria for demonstrations of
Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A, 40, 913
(1989)]. We develop a general theory of experimental EPR-steering criteria,
derive a number of criteria applicable to discrete as well as
continuous-variables observables, and study their efficacy in detecting that
form of nonlocality in some classes of quantum states. We show that previous
versions of EPR-type criteria can be rederived within this formalism, thus
unifying these efforts from a modern quantum-information perspective and
clarifying their conceptual and formal origin. The theory follows in close
analogy with criteria for other forms of quantum nonlocality (Bell-nonlocality,
entanglement), and because it is a hybrid of those two, it may lead to insights
into the relationship between the different forms of nonlocality and the
criteria that are able to detect them.
