  We show that the combination of spin-orbit coupling with a Zeeman field or
strong interactions may lead to the formation of a helical liquid in
single-channel quantum wires. In a helical liquid, electrons with opposite
velocities have opposite spin precession. We argue that zero-energy Majorana
bound states are formed in various situations when the wire is situated in
proximity to a conventional s-wave superconductor. This occurs when the
external magnetic field, the superconducting gap, or, in particular, the
chemical potential vary along the wire. We discuss experimental consequences of
the formation of the helical liquid and the Majorana bound states.
