The past decade has witnessed an explosive activity in the study of disorderly growth phenomena. Much of the impetus behind these investigations has been the realization that random growth processes often lead to the formation of self-similar or self-affine fractal patterns. Significant progress has been achieved by studying simplified models with rich dynamical properties and finding scaling laws using various theoretical considerations. The most important aspect of these developments is that through fractal concepts it has recently become possible to describe a variety of far-from- equilibrium phenomena, which, despite their importance, until the last decade had not been investigated intensively because they were viewed as intractable.