This paper introduces the HEX (High-pressure Elemental Xstals) database, a complete database of the ground-state crystal structures of the first 57 elements of the periodic table, from H to La, at 0, 100, 200 and 300 GPa. HEX aims to provide a unified reference for high-pressure research, by compiling all available experimental information on elements at high pressure, and complementing it with the results of accurate evolutionary crystal structure prediction runs based on Density Functional Theory. Besides offering a much-needed reference, our work also serves as a benchmark of the accuracy of current ab-initio methods for crystal structure prediction. We find that, in 98% of the cases in which experimental information is available, ab-initio crystal structure prediction yields structures which either coincide or are degenerate in enthalpy to within 300 K with experimental ones. The main manuscript contains synthetic tables and figures, while the Crystallographic Information File (cif) for all structures can be downloaded from the related figshare online repository.