Elastic wave velocities and densities of iron and candidate iron alloys are important properties for understanding the seismological observations of Earth’s core. Several methods have been applied to measure the elastic wave velocities of iron and iron alloys at room temperature. Recently, measurements have been extended to simultaneous high-pressure and high-temperature conditions. Birch’s law, which is the linearity between density and compressional wave velocity (VP), is applicable to the experimental results of density and VP at high pressure and room temperature. The effect of temperature on Birch’s law is discussed, and it is not negligible at temperatures greater than 1,000–2,000 K. The VP and density of hcp Fe are extrapolated to pressure and temperature conditions of the inner core. VP of hcp Fe at 330–360 GPa is higher than the inner core seismic velocity, thus suggesting that iron should be alloyed with other elements so as to reduce not only its density, but also its velocity at inner core conditions. The VP of Fe–Si, Fe–H, and Fe–C alloys is slower than that of Fe at the pressure of the inner core. If the temperature effect on Birch’s law is taken into account, Si and H can be candidates for the major light elements in the inner core, while C, O, and S may not be included or exist as minor constituents.