Recently, three-dimensionally laterally confined semiconductor quantum wells ('quantum dots') have been realized. These structures are analogous to semiconductor atoms, with energy level separation of order 25 meV, and tunable by means of the confining potentials. A systematic study reveals a (radius)^-1 dependence on the energy separation. The electronic transport through quantum dots is presented and analysed. The spectra correspond to resonant tunnelling from laterally confined emitter contact subbands through the discrete three-dimensionally confined quantum dot states. The effects of two dots in series, and Fermi level effects, are presented.