We describe how magnetotunneling spectroscopy can be used to investigate the spatial form of the wave function of confined electron states in self-assembled InAs quantum dots grown on (100)- and $(311)B$-oriented GaAs substrates. For both orientations, the wave function is found to have a biaxial symmetry in the growth plane, with axes parallel to the main crystallographic directions. We also present magnetotunneling spectroscopy measurements in a multiple-terminal resonant-tunneling device, which incorporates a series of gate electrodes. The gates allow us to address an individual dot electrostatically, and to identify and measure its energy levels and associated wave functions. The limitations and possible future applications of the technique are also discussed.