Adaptive (path dependent) processes of growth modeled by urn schemes are important for several fields of applications: biology, physics, chemistry, economics.
In this paper we present a review of studies that have been done in the technological dynamics by means of the urn schemes. Also several new macroeconomic models of technological dynamics are analysed by the same machinery and its new modification allowing to tackle non-homogeneity of the face space. We demonstrate the phenomena of multiple equilibria, different convergence rates for different limit patterns, locally positive and locally negative feedbacks, limit behavior associated with non-homogeneity of economic environment where producers (firms) are operating