The concept of Adaptive Control can be traced back to the early fifties and it can be understood as the control of systems partially known. All natural and artificial dynamical systems are subjected, up to some extent, certain degree of unknown behavior expressed in terms of parameters uncertainty, external or internal perturbations and time varying properties, whose effects on the system could cause abnormal or even unstable functioning.In this paper we summarize the main techniques and results developed by our research group over the last years for analyzing identifying and controlling adaptive systems, presenting the most important contributions to the field developed by our group. Besides, we present some interesting applications in the engineering field where these techniques have been successfully applied at simulation as well as practical levels.