The (trivalent) lanthanides exhibit a common sequence of phases upon the application of pressure: hcp → dhcp → fcc → “distorted-fcc”. The “distorted-fcc”’ phase (d-fcc), observed in the light lanthanides is known to be related by geometric distortions to the fcc unit cell, yet the d-fcc phase has been reported to comprise of one or two structures, with no prevailing consensus as to the solution(s). This thesis contains a detailed study of the d-fcc phase of the light lanthanides Pr and Nd. High-pressure angle-dispersive powder-diffraction techniques were employed to systematically study the phases adopted by Pr (up to 25GPa) and Nd (up to 44GPa). Particular attention was paid to solving the d-fcc of each of these elements, the structure of which is very unclear in published work. In Pr, the d-fcc between 7 and 20GPa is shown to comprise of two phases, the solutions of which are shown to be hR24 (R¯3m) and oC16 (Ibam) for the regions 7-14GPa and 14-20GPa, respectively. The pressure dependence of each of these structures over their stability range is presented. Revisions to previously-published volume vs. pressure data are made, with a different value for the volume collapse at the 4f electron delocalisation transition reported. Similarly, the d-fcc phase of Nd, stable over the pressure range 16-40GPa, is studied in detail. Nd differs from Pr by undergoing a further transition, to a hP3 (P63) structure, on pressurisation above 40GPa, before transforming to a α-Uranium phase. The distorted-fcc phase is shown, like that of Pr, to comprise of two phases, hR24 (R¯3m) and oC16 (Ibam) for the pressure regions 16-26GPa and 26-40GPa, respectively. Data on Nd are presented up to the maximum pressure achieved, 44GPa. Data from a preliminary study of La are also presented, along with a brief report on attempts to prepare a single crystal of Pr within a diamond anvil cell, by laser annealing of a powder of Pr.