Viscosity is an important rheological property of metals in casting because it controls the rate of transport of liquid metals, which may lead to casting defects such as hot tearing and porosity. The measurement methods and numerical models of the viscosity of liquid and semi-solid state metals that have been published to date are reviewed in this paper. Most experimental measurements have been performed with rotational and oscillatory viscometers, which offer advantages at low viscosities in particular. Besides these two traditional methods for measuring viscosities, a couple of studies also introduced the technique of isothermal compression for alloys in the semi-solid state, and even an optical basicity method for the viscosity of slags. As to numerical models, most published results show that the viscosity of liquid and semi-solid state metals can be described by the Arrhenius, Andrade, Kaptay or Budai-Bemk-Kaptay equations. In addition, there are some alternative models, such as the power model and the isothermal stress-strain model.