This second article on ionizing radiation covers the science of the measurement of radioactivity (radionuclide metrology). In common with radiation dosimetry, radionuclide metrology is an application-led science: the use of radionuclides in medical imaging and cancer therapy, the need to ensure safe disposal of radioactive wastes from the nuclear power industry and the requirement for worldwide monitoring systems to detect nuclear weapons tests all drive the development of primary standards and reference materials to ensure accurate measurement. After a short overview of the physics of radioactive decay, the methods used to realize primary standards are described, including the techniques that use recent developments in mathematical modelling and digital signal processing for radionuclides with complex decay schemes. The international measurement system for radionuclide metrology is summarized. The article concludes with a summary of the future challenges for the field, including how the skills of both dosimetrists and radionuclide metrologists are being called on to ensure safe and effective cancer treatment using a new class of drugs.