Quantum gases/fluids, such as the Bose-Einstein condensates (BEC) in cold atoms and superfluid helium, demonstrate macroscopic quantum phenomena, and one of them is quantum vortex. Quantum turbulence can be considered as a state of quantum fluids with a large number of tangled quantum vortices. We study the formation and dynamics of quantum vortices via the nonlinear Klein-Gordon equation (NLKG), as well as their applications in high energy physics and cosmology. The non-relativistic limit of NLKG naturally leads to the nonlinear Schrodinger equation/Gross-Pitaevskii equation, which has been intensively used in describing the BEC of cold atoms.