  Bell nonlocality between distant quantum systems---i.e., joint correlations
which violate a Bell inequality---can be verified without trusting the
measurement devices used, nor those performing the measurements. This leads to
unconditionally secure protocols for quantum information tasks such as
cryptographic key distribution. However, complete verification of Bell
nonlocality requires high detection efficiencies, and is not robust to the
typical transmission losses that occur in long distance applications. In
contrast, quantum steering, a weaker form of quantum correlation, can be
verified for arbitrarily low detection efficiencies and high losses. The cost
is that current steering-verification protocols require complete trust in one
of the measurement devices and its operator, allowing only one-sided secure key
distribution. We present device-independent steering protocols that remove this
need for trust, even when Bell nonlocality is not present. We experimentally
demonstrate this principle for singlet states and states that do not violate a
Bell inequality.
