Vertical-cavity surface-emitting lasers (VCSELs) yield single-longitudinal-mode operation, low-divergence circular output beam, and low threshold current. This paper gives an overview on theoretical, self-consistent modelling of physical phenomena occurring in a VCSEL. The model has been experimentally confirmed. We present versatile numerical methods for nitride, arsenide, and phosphide VCSELs emitting light at wavelengths varying from violet to near infrared. We also discuss different designs with respect to optical confinement: gain guidance using tunnel junctions and index guidance using oxide confinement or photonic crystal and we focus on the problem of single-transverse-mode operation.