We present a new approach to adaptive nonlinear control based on a complete controller-identifier separation which has long been a goal in adaptive system design. Our controllers guarantee certain input/state stability properties with respect to the parameter error $\tilde\theta$ and its derivative $\dot{\tilde\theta}$ as inputs. The parameter identifiers, in turn, guarantee $\tilde\theta\in{\cal L}_\infty$, and either $\dot{\tilde\theta}\in{\cal L}_\infty$ or $\dot{\tilde\theta}\in{\cal L}_2$ or both. This estimation-based approach encompases two families of schemes: swapping-based and observer-based. Swapping-based schemes allow the use of a wide variety of update laws --- gradient and least-squares, normalized and unnormalized. Observer-based schemes use parameter identifiers of lower dynamic order. All these schemes achieve systematic improvement of transient performance.