This book describes the progress that has been made toward the development of a comprehensive understanding of the formation of complex, disorderly patterns under far from equilibrium conditions. It describes the application of fractal geometry and scaling concepts to the quantitative description and understanding of structure formed under nonequilibrium conditions. Self similar fractals, multi-fractals and scaling methods are discussed, with examples, to facilitate applications in the physical sciences. While the emphasis is on computer simulations and experimental studies, the author also includes discussion of theoretical advances in the subject. Much of the book deals with diffusion-limited growth processes and the evolution of rough surfaces, although a broad range of other applications is also included. This book will be of interest to graduate students and researchers in physics, chemistry, materials science, engineering and the earth sciences, particularly those interested in applying the ideas of fractals and scaling.