Abstract : Fractals, as introduced by Benoit Mandelbrot over ten years ago, are scale self-similar mathematical objects possessing nontrivial geometrical properties. There exist various physical realizations of fractals, and here we shall consider what we believe to be one of the most important such realizations, namely, fractal; clusters. Attention will be paid mainly to their optical properties. A fractal cluster is a system of interacting material particles called monomers. Theory of linear optical properties of fractal clusters is developed in this report. The theory is based upon the exact properties of dipole polarizability and assumption of the existence of scaling for the dipole excitations (eigenstates) of the fractal. This assumption is self-consistently validated by the results of the theory and is also confirmed by numerical stimulation in the framework of the Monte-Carlo method. Using exact relations and the scaling requirements, it is shown that the fractal absorption and density of eigenstates scale with the same exponent d sub o-1.