[en] We have studied with neutron scattering techniques betaine calcium chloride dihydrate (BCCD), a dielectric aperiodic crystal which displays a Devil's staircase type phase diagram made up of several incommensurate and commensurate phases, having a range of stability very sensitive to temperature, electric field and hydrostatic pressure. We have measured a global hysteresis of δ(T) of about 2-3 K in the two incommensurate phases. A structural study of the modulated commensurate phases 1/4 and 1/5 allows us to evidence that the atomic modulation functions are anharmonic. The relevance of the modelization of the modulated structure by polar Ising pseudo-spins is then directly established. On the basis of group theory calculation in the four dimensional super-space, we interpret this anharmonic modulation as a soliton regime with respect to the lowest-temperature non modulated ferroelectric phase. The continuous character of the transition to the lowest-temperature non modulated phase and the diffuse scattering observed in this phase are accounted for the presence of ferroelectric domains separated by discommensurations. Furthermore, we have shown that X-rays induce in BCCD a strong variation with time of irradiation of the intensity of satellite peaks, and more specifically for third order ones. This is why the 'X-rays' structural model is found more harmonic than the 'neutron' one. Under electric field applied along the vector b axis, we confirm that commensurate phases with δ = even/odd are favoured and hence are polar along this direction. We have evidenced at 10 kV / cm two new higher order commensurate phases in the phase INC2, corroborating the idea of a 'complete' Devil's air-case phase diagram. A phenomenon of generalized coexistence of phases occurs above 5 kV / cm. We have characterized at high field phase transitions between 'coexisting' phases, which are distinguishable from classical lock-in transitions. Under hydrostatic pressure, our results contradict the pressure - temperature phase diagrams previously determined or extrapolated above room-temperature. (author)