An attempt is made to trace the evolution of the inverting eyepiece from a simple convex lens to the very elaborate modern systems employing as many as seven component lenses. The conditions that an eyepiece should satisfy are stated with special reference to the `Petzval sum', the apparent field of view, the exit pupil and the eye clearance. Reference is also made to the use of aspherical refracting surfaces and to the simplification of design that may be expected to result from their use. Finally, constructional details of various known types of eyepiece are given in the form of a table.