The paper selectively surveys three sets of models and their applications in modelling technological change. More than one half of output growth of most countries in the twentieth century is attributed to technological change. Yet, the understanding of this subject is still elusive to economists. Technology has a morphogenic influence over the economic system because over time technological parameters are changing the shape and form of the economic system itself. To understand such systems qualitative models are needed Three models of morphogenesis along with their applications in modelling technological change are presented. These are the logistic growth, the reaction-diffusion and the catastrophe models. It is concluded that nonlinear dynamic models are increasingly useful in enhancing our understanding of the various facets of technological change, such as the generation, diffusion, and impact of the new technologies.