The kilogram is the last remaining SI unit defined by an artefact—the platinum–iridium cylinder kept at the International Bureau of Weights and Measures (BIPM). The artefact standard is subject to, admittedly very small, irreversible changes caused both by wear and by accretion of mass from atmospheric pollutants. In addition, the unit of mass can only be disseminated by comparison with the artefact held by the BIPM. Comparisons of its mass with other similar and equally carefully preserved cylinders show relative changes, over many tens of years, of several parts in 10⁸. If a procedure was available to link mass to a fundamental constant, with a similar or better accuracy, the above limitations would be overcome, making the unit accessible to anyone caring to carry out the procedure and long term stability would be assured. Attempts to do this fall into two broad categories: the first relates the kilogram to atomic masses by measuring the number of atoms in a sample and the second relates the kilogram to Planck's constant, the metre and the second via the equivalence of mechanical and electrical energy. We summarize experiments in both these categories.