We review recent experimental advances by the Buffalo group in performing far-infrared magnetospectroscopy under he tuning of applied high hydrostatic pressure. Experiments are reported for the effects of pressure on Si donors in modulation doped GaAs/AlGaAs quantum wells. We clearly observe pressure-mediated competition between free (i.e., Landau level) and bound electron states -the latter arising from both neutral (D 0 ) and charged (D -) donor species. With increasing pressure, there is a progression of the observed spectra from being dominated by cyclotron resonance and the D -singlet (or singlet-like bound magnetoplasmon) transitions, to showing the D0 is →2p+ line. The main reason for this evolution is the decrease in electrons due to the crossover of the Si levels associated with the F (well) and X (barrier) conduction minima. Indeed, for pressures above 30 kbar the Γ(well)-X(barrier) crossover quenches all the transitions. However, we find strong evidence that electrons are independently lost to a trap, which becomes active several kbar below this crossing. A possible candidate for this trap is residual Se impurities in the barriers. We present the results of detailed numerical calculation which are found to agree very well with the measured field dependencies of the cyclotron resonance, D0 and D -transition energies. In the sample with the highest doping, a new transition is observed for fields and pressures above 7.5 T and 5 kbar. Reasons for this apparent anomaly are discussed.