A brief survey of some results concerning optical and electrical properties of discontinuous metal films on dielectric substrates and their statistical description is given. Optical properties (transmittance and imaginary part of dielectric permittivity spectra) of Al, Cu and Mn discontinuous films are presented and interpreted in terms of effective medium theories; modified Maxwell-Garnett and Bruggeman. The ranges of dielectric properties, the percolation threshold, and the range of metallic properties are determined for optical and electrical properties of the film examined. The considerations concerning electrical properties include such conduction mechanisms as metal conduction, substrate conduction, quantum tunneling, thermally activated tunneling and hopping. Real structures of the films are examined making use of electron microscope. Also the computer model for determining the contribution of the fundamental conduction mechanisms in discontinuous films is introduced. The inverse power law is used to describe the structure and the statistical distributions of inhomogeneous films of Au, Cu and Mn on dielectric substrates. To this end, the rank of an island is connected with its area for the films with different coverage coefficients (metal content). The dependencies of the island areas on the rank orders in a double-logarithmic plot are straight lines according to the Mandelbrot law. The slope of the straight line characterises the ranges of the distributions of the islands: (i) the log-normal or the Gaussian one (with two parameters of statistical distribution-the mean value and the variance), (ii) the Poisson distribution (with one parameter-the mean value), (iii) Levy stable distribution (the parameters of distribution are infinite). The correlation between optical and electrical properties of discontinuous metal films and their structures and statistical description is found.