  Correlations between distant particles are central to many puzzles and
paradoxes of quantum mechanics and, at the same time, underpin various
applications like quantum cryptography and metrology. Originally in 1935,
Einstein, Podolsky and Rosen (EPR) used these correlations to argue against the
completeness of quantum mechanics. To formalise their argument, Schr\"odinger
subsequently introduced the notion of quantum steering. Still, the question
which quantum states can be used for the EPR argument and which not remained
open. Here we show that quantum steering can be viewed as an inclusion problem
in convex geometry. For the case of two spin-$\frac{1}{2}$ particles, this
approach completely characterises the set of states leading to the EPR argument
and consequently to a full description of the quantum correlations that can be
used for steering. Our results find applications in various protocols in
quantum information processing, and moreover they are linked to quantum
mechanical phenomena such as uncertainty relations and the question which
observables in quantum mechanics are jointly measurable.
