The concept of Adaptive Systems can be trace back to the early fifties and they can be understood as systems with partially known characteristics. All natural and artificial dynamical systems exhibit up to some extent certain degree of unknown behavior expressed in terms of parameters uncertainty, external or internal perturbations and time varying properties. On the other hand, having all the necessary knowledge on a system for analysis, design, and control purposes is quite unusual. All natural and artificial systems present some kind of unknown behavior whose effects on the system could cause abnormal behaviors or even its destruction. In this talk we summarize the main techniques developed along the time for analysis, identification and control of adaptive systems, presenting the most important results developed by the control community and our contributions to the field. Beside we present some interesting applications in the engineering field where these techniques have been applied. The talk starts with the case of simple linear dynamical systems of integer order up to the most recent results obtained which involve concept of fractional order and nonlinear dynamical systems.