Viscosity ratio measurements made with capillary viscometers exploit the accurate values of the viscosity of helium calculated ab initio. Accurate values of the argon-to-helium viscosity ratio are now used for primary acoustic gas thermometry and for the most accurate redeterminations of the Boltzmann constant. Accurate viscosity ratio measurements enable the calibration of laminar flow meters with surrogate gases and their use with process gases. We review ratio viscometers that comprise one, two, and four capillaries. A single capillary is a ratio viscometer when it is used to measure multiple gases sequentially, while two- and four-capillary viscometers are instruments intended for ratio measurements. We consider gases and Newtonian liquids, with a focus on the two-capillary gas viscometer and its extension to pressures up to 100 MPa. A single-capillary viscometer could measure the ratio (viscosity of liquid water)/(viscosity of gaseous helium) thereby reducing the uncertainty of the liquid viscosity scale relative to the international system of units.