Since the first experimental realization of an atomic Bose Einstein condensate (BEC), awarded the Nobel Prize in 2001, the properties of this superfluid system have been intensively studied both experimentally and theoretically. Performing three-dimensional numerical simulations using real physical parameters remains a challenging task for providing complementary information to experimental observations.

We first give an introduction to classical mathematical models (Gross-Pitevskii theory) to describe Bose-Einstein condensates in the zero temperature limit. 
Numerical challenges to simulate 3D configurations with vortices are then discussed.

Finally, we present different numerical set-ups (6th order finite difference schemes, finite elements with mesh adaptivity, spectral methods) and numerical results corresponding to configurations with vortices observed in physical experiments: single-line vortex, Abrikosov lattice, giant vortex. New configurations with arrays of condensates in 1D rotating optical lattices are also presented.