The resonant tunnelling diode experiments stimulated several different semiclassical descriptions of the observed oscillations in the tunnelling current. It appears that the only approach providing the quantitative description over most experimental regimes is the approach using complex non-periodic orbits. The main result of the paper is a general semiclassical formula for the current in the resonant tunnelling diode. Numerical comparisons with quantal calculations and experiment are carried out. The techniques used in this paper can also be applied to other problems, for example, to Franck-Condon spectra.