This special issue is intended to present a review of mass standards, mass determination and the efforts to replace the international prototype of the kilogram by a new definition of the kilogram based on a fundamental constant of physics.

Mass is a quantity that is familiar to everybody primarily for its importance in commerce. It is not only one of the traditional quantities of metrology but also of science in general. The unit of mass has always been based on a material object and, since 1889, on the international prototype of the kilogram. The mass of any standard weight is derived from this prototype by a cascade of comparison measurements using balances. The sources of uncertainty of the mass of a standard depend upon the circumstances of the weighing process and the long-term instabilities of the intermediate standards. The international prototype—its mass is one kilogram by definition—may also suffer from instabilities or drifts in time, but until now it has not been possible to check this by comparison with a fundamental constant in physics. Repeated verifications of some 40 or so national prototypes of the members of the Metre Convention have shown significant drifts with an average of about 50 µg within 100 years, a fact that casts doubt on the stability of the international prototype itself. Experiments have been underway for about 30 years on linking fundamental constants such as the Avogadro constant or, correspondingly, the atomic mass unit and Planck's constant to the kilogram. Relative uncertainties of the order of 10^-7 have been reached today, still one order of magnitude too large for monitoring the stability of the international prototype or for a new definition.

The first article of this special issue gives information on the international and the national prototypes of the kilogram, its material, manufacture, cleaning procedures, stability investigations and the periodic verifications of national prototypes.

The next article describes methods for determining the mass of multiples and submultiples of the kilogram. In practice, mass standards in the range from one milligram up to several thousands of kilograms are used for the mass determination of commercial objects or for the calibration of weighing instruments. The determination of the mass of multiples and submultiples of the kilogram is a procedure that links such mass standards to the kilogram by a number of—mostly redundant—weighing processes and mathematical procedures that result in the values and the uncertainties of the standards involved.

The reproducibility of E-class weights is the topic of the next article. Classification of weights is defined in an international recommendation for legal metrology and is carried over into the national regulations of most countries. E-class weights are at the highest level in this context. Reproducibility is related to the instability of mass standards within some time interval. Corresponding observations and discussions of the results are reported.

As already mentioned, weighing is an important source of the uncertainty of a mass standard. The requirements on weighing in legal metrology are discussed in the following article. It refers to the project of a new international recommendation for weights (revised OIML R 111) that describes procedures for mass determination and for testing the properties of weights according to the stated requirements for the different classes.

The instability of mass standards is mostly due to surface contamination. A review of the stability of platinum–iridium and stainless-steel standards and their surface contamination is presented in the next article. It gives a comprehensive overview of published data and investigations on this topic.

Magnetic weights interact with the magnetic field generated by a balance. A change in the balance indication is the consequence if certain limits are exceeded. Magnetic properties of weights, their measurements and magnetic interactions between weights and balances constitute the theme of the next article. After an introduction to the theoretical aspects of magnetic fields and magnetic forces, different measurement methods, international comparisons in this field, modelling the interacting forces and finally the impact on the new international recommendation for weights are presented.

The moving-coil Watt balance and the superconducting magnetic levitation experiment are two of the experiments aimed at redefining the kilogram. 'Tracing Planck's constant to the kilogram by electromechanical methods' is the title of the corresponding article. It describes the principles of these experiments and reviews the efforts and results achieved at present in the laboratories concerned.

Another approach to redefining the kilogram is reviewed in the article entitled 'Tracing the definition of the kilogram to the Avogadro constant using a silicon single crystal'. This approach is performed in a worldwide collaboration coordinated by the Working Group on the Avogadro Constant of the CIPM Consultative Committee for Mass and related quantities.

An experiment for determining the atomic mass unit by ion accumulation follows a straightforward way for determining the mass of an atom by collecting ions, weighing and 'counting' them by measuring their total charge. This article reports on a 'third' way of redefining the kilogram. This approach is followed by only one laboratory and it is still at an early stage compared with the uncertainties already achieved by the other ones.