The two-spiral task is a well-known benchmark for binary classification. The data consist of points on two intertwined spirals which cannot be linearly separated. This article reviews how this task and some of its variations have significantly inspired the development of several important methods in the history of artificial neural networks. The two-spiral task became popular for several different reasons: (1) it was regarded as extremely challenging; (2) it belonged to a suite of standard benchmark tasks; and (3) it had visual appeal and was convenient to use in pilot studies. The article also presents an example which demonstrates how small variations of the two-spiral task such as relative rotations of the two spirals can lead to qualitatively different generalisation results.