The majority of the metallic elements adopt simple, high-symmetry structures at ambient pressure. These consist of a highly-ordered arrangement of atoms, which can be described by a crystal lattice that is periodic in three dimensions. It may be expected that close-packed structures, such as face-centred cubic (fcc) and hexagonal close-packed (hcp), would be favoured at high pressures due to the increase in density. However, many of these elements transform to lowsymmetry, complex structures on compression. In particular, a number have been observed to adopt incommensurately-modulated structures at high pressure. In these structures, atoms are displaced from their average positions by a modulation wave, the wavelength of which is an irrational multiple of the lattice periodicity. Diamond-anvil cells (DACs) can be used to compress materials to over a million times atmospheric pressure. In these devices, a small sample is compressed between the tips of two diamond anvils. The atomic arrangement of materials at extreme pressures can then be probed using the intense x-ray beams provided by synchrotron sources. In this work, the high-pressure crystal structures of the lanthanide elements europium (Eu) and samarium (Sm) have been investigated using angle-dispersive x-ray powder dffraction techniques. The high-pressure structural behaviour of Eu has been found to be remarkably different from that of the other lanthanide elements. Two new high-pressure phases of Eu are reported, both of which have an incommensurately-modulated crystal structure.