Accurate determination of elements in various kinds of samples is essential for many areas, including environmental science, medicine, as well as industry. Inductively coupled plasma mass spectrometry (ICP-MS) is a powerful tool enabling multi-elemental analysis of numerous matrices with high sensitivity and good precision. Various calibration approaches can be used to perform accurate quantitative measurements by ICP-MS. They include the use of pure standards, matrix-matched standards, or relevant certified reference materials, assuring traceability of the reported results. This review critically evaluates the advantages and limitations of different calibration approaches, which are used in quantitative analyses by ICP-MS. Examples of such analyses are provided.This article is part of the themed issue ‘Quantitative mass spectrometry’.