Plane patterns, both one-color and two-color, can be naturally classified according to the symmetries they admit. In this survey the symmetries of the plane, and the resulting classification of patterns, are described. Following the lead of A. Speiser and E. Mueller the author studied patterns in various African contexts, and in the American Southwest, culminating in the book Symmetries of Culture with Dorothy Washburn. The results of field trips to Fiji and Tonga, applying the techniques from that book, are described and illustrated.