This paper reviews studies on gillnet selectivity: the relevant characteristics of fish and nets, graphical and mathematical representation of selectivity curves, and methods of estimation. F. I. Baranov started these studies 60 yr ago, and most subsequent work has been consistent with his axioms that a) gillnets catch fish whose head girths are smaller but maximum girths larger than the mesh perimeter, and b) selectivity curves for all mesh sizes have the same shapes and heights. Unfortunately these axioms are inaccurate. The heights of selectivity curves increase with mesh sizeSelectivity depends mainly on fish size and shape and mesh size, but is also affected by the thickness, material, and color of net twine, hanging of net, and method of fishing. The left slopes of selectivity curves represent smaller fish wedged in the meshes; the right slopes, larger fish mainly tangled by head parts. The curves may be very skewed or multimodal for fish that are easily tangled.The most reliable, though expensive, estimates of gillnet selectivity are by "direct" methods of fishing a population of known size-frequency distribution. The more popular but biased "indirect" estimates compare catches by two or more mesh sizes. Other methods used are prediction from girth measurements and the DeLury method.