This chapter covers the necessary physics to understand the problem and dynamics of quantized vortices and their corresponding energy spectra. It starts by deriving the hydrodynamics equations from the nonlinear Schrödinger equation using the Madelung transform. The chapter mainly focuses on vortex dynamics, especially regarding quantum fluids. The discussion includes vorticity, circulation and vortex dynamics in Schrödinger fluids, comparing vortex rings classical and Schrödinger fluids as well as covering vortex reconnections, Crow instability, Kelvin waves and energy spectra. The chapter concludes by talking about vortex stretching during vortex reconnections, emphasizing its importance in transferring energy from large to small scales which in part contributes to the Kolmogorov k−5/3 scaling.