The phase diagrams of Ce, Th, and Pu metals have been studied by means of density-functional theory (DFT). In addition to these metals, the phase stability of Ce-Th and Pu-Am alloys has been also investigated from firstprinciples calculations. Equation-of-state (EOS) for Ce, Th, and the Ce-Th alloys has been calculated up to 1 Mbar pressure in good comparison to experimental data. Present calculations show that the Ce-Th alloys adopt a body-centered-tetragonal (bct) structure upon hydrostatic compression which is in excellent agreement with measurements. The ambient pressure phase diagram of Pu is shown to be very poorly described by traditional DFT but rather well modelled when including magnetic interactions. In particular, the anomalous δ phase of Pu is shown to be stabilized by magnetic disorder at elevated temperatures. The Pu-Am system has also been studied in a similar fashion and it is shown that this system, for about 25% Am content, becomes antiferromagnetic below about 400 K which corroborates the recent discovery of a Curie-Weiss behavior in this system.