  We investigate superfluidity, and the mechanism for creation of quantized
vortices, in the relativistic regime. The general framework is a nonlinear
Klein-Gordon equation in curved spacetime for a complex scalar field, whose
phase dynamics gives rise to superfluidity. The mechanisms discussed are local
inertial forces (Coriolis and centrifugal), and current-current interaction
with an external source. The primary application is to cosmology, but we also
discuss the reduction to the non-relativistic nonlinear Schr\"{o}dinger
equation, which is widely used in describing superfluidity and vorticity in
liquid helium and cold-trapped atomic gases.
