This review deals principally with the interaction between double-diffusive convection and an externally imposed vertical magnetic field in a Boussinesq fluid. Both linear and nonlinear (two and three-dimensional) theories have been discussed. Double-diffusive magnetoconvection is shown to exhibit a rich variety of dynamical behaviour unimaginable in a single component system and serves as a guide to the behaviour of all triple-diffusive systems. Finally, the effects of cross-diffusion, rotation and chemical reaction on double-diffusive magnetoconvection and pattern selection have been briefly touched upon.