We report a comprehensive study of the effects of self-consistency on the I-V-characteristics of resonant tunnelling structures. The calculational method is based on a simultaneous solution of the effective-mass Schrödinger equation and the Poisson equation, and the current is evaluated with the Tsu-Esaki formula. We consider the formation of the accumulation layer in the emitter contact layer in a number of different approximation schemes, and we introduce a novel way to account for the energy relaxation of continuum states to the two-dimensional quasi-bound states appearing for contain applied voltages and carrier densities at the emitter-barrier interface. We include the two-dimensional accumulation layer charge and the quantum well charge in our self-consistent scheme. We discuss the evaluation of the current contribution originating from the two-dimensional accumulation layer charges, and our qualitative estimates seem consistent with recent experimental studies. The intrinsic bistability of resonant tunnelling diodes is analyzed within several different approximation schemes.