For measuring machines and machine tools, geometrical accuracy is a key performance criterion. While numerical compensation is well established for CMMs, it is increasingly used on machine tools in addition to mechanical accuracy. This paper is an update on the CIRP keynote paper by Sartori and Zhang from 1995 [Sartori S, Zhang GX (1995) Geometric error measurement and compensation of machines, Annals of the CIRP 44(2):599–609]. Since then, numerical error compensation has gained immense importance for precision machining. This paper reviews the fundamentals of numerical error compensation and the available methods for measuring the geometrical errors of a machine. It discusses the uncertainties involved in different mapping methods and their application characteristics. Furthermore, the challenges for the use of numerical compensation for manufacturing machines are specified. Based on technology and market development, this work aims at giving a perspective for the role of numerical compensation in the future.