  Quantum correlations between two parties are essential for the argument of
Einstein, Podolsky, and Rosen in favour of the incompleteness of quantum
mechanics. Schr\"odinger noted that an essential point is the fact that one
party can influence the wave function of the other party by performing suitable
measurements. He called this phenomenon quantum steering and studied its
properties, but only in the last years this kind of quantum correlation
attracted significant interest in quantum information theory. In this paper the
theory of quantum steering is reviewed. First, the basic concepts of steering
and local hidden state models are presented and their relation to entanglement
and Bell nonlocality is explained. Then various criteria for characterizing
steerability and structural results on the phenomenon are described. A detailed
discussion is given on the connections between steering and incompatibility of
quantum measurements. Finally, applications of steering in quantum information
processing and further related topics are reviewed.
