Owing to the spectacular currency of information and communication technologies, the diffusion of innovations has become one of the most exciting research topics in the social sciences in the past decade. This study gives an account of the most basic types of growth functions, and then inspects the broad applications of this diffusion of technological innovations. The second half of the study surveys the endeavors which seek to apply the use of growth functions to the broadest possible areas of social change via the long waves of economic development and logistic substitution processes.