This survey paper aims, to present in a systematic way, the 'state-of-the-art' of a class of so called optimized adaptive control methodologies, where adaptive systems theory is complemented by optimal control theory. It is based on literature published since 1958 and emphasizes results with proven industrial relevance. After recalling previous adaptive systems, results that had prepared the ground for the new ideas, the analysis departs from the work on adaptive predictive control in the mid 1970s, which provided the conceptual basis for the development of this kind of technique. Well-known design methods, both from the stability and optimization perspectives, along with their results, are interpreted in an intuitive way in order to understand how control law and the adaptive mechanism complement each other to produce mature controllers that can reliably solve the industrial process dynamic stabilization problem. Surveys of industrial applications from both design perspectives are presented and industrial products based on optimized adaptive control are cited.