The properties of element 92, uranium, at low temperature have remained an enigma since major anomalies in almost all physical property measurements were first reported over twenty years ago. By far the most dramatic measurements were those by Fisher on the elastic constants, which strongly suggested a structural phase transition at ≈ 43 K. Initially no such phase transition was found. Recently, neutron inelastic experiments at Oak Ridge mapped out the phonon dispersion curves at room temperature, and in the process discovered an anomously soft phonon of Σ 4 symmetry along the [100] axis. On cooling, weak satellites were found to form near the position [0.5, 0, 0] thus signaling a periodic distortion. However, such a charge-density wave appeared to have a complex wave vector relationship with the fundamental lattice, leading the authors to introduce a two-phase model for the phase transition. Simultaneously, by using photographic techniques designed to view large segments of reciprocal space, Marmeggi and Delapalme at the ILL discovered a completely new set of satellite reflections, indexable with wave vector [0.5, q y , q z ], where q y and q z are incommensurable (≈0.18), not equal, and vary with temperature. We have now measured the intensities of a great number of these new satellites and been able to fit the results with a modulated α-U structure. The atoms are displaced in all three independent crystallographic directions according to a sinusoidal wave form. The overall agreement between the predicted and observed structure factors is excellent, suggesting that at least the static positions of the atoms at low temperature in this element are now understood. In this review the status of research on the structural phase transition will be presented. Neither the full details of the phase transition nor the reasons for it are understood at this time. A number of further experiments are suggested.