  Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which
is intermediate between entanglement and Bell nonlocality. EPR steering is a
resource for quantum key distribution that is device independent on only one
side in that it certifies bipartite entanglement when one party's device is not
characterized while the other party's device is fully characterized. In this
work, we introduce two types of genuine tripartite EPR-steering, and derive two
steering inequalities to detect them. In a semi-device-independent scenario
where only the dimensions of two parties are assumed, the correlations which
violate one of these inequalities also certify genuine tripartite entanglement.
It is known that Alice can demonstrate bipartite EPR-steering to Bob if and
only if her measurement settings are incompatible. We demonstrate that quantum
correlations can also detect tripartite EPR-steering from Alice to Bob and
Charlie, even if Charlie's measurement settings are compatible.
