Many archaeological patterns are fractal. Fractal analysis, therefore, has much to contribute to archaeology. This article offers an introduction to fractal analysis for archaeologists. We explain what fractals are, describe the essential methods of fractal analysis, and present archaeological examples. Some examples have been published previously, while others are presented here for the first time. We also explain the connection between fractal geometry and nonlinear dynamical systems. Fractals are the geometry of complex nonlinear systems. Therefore, fractal analysis is an indispensable method in our efforts to understand nonlinearities in past cultural dynamics.