An interesting phenomenon occurs when one attempts to control systems with output nonlinearity growing faster than linearity, where similarities between the continuous- and discrete-time cases of adaptive control no longer exist. It is generally known that a large class of continuous-time nonlinear parametric systems, regardless of how fast the growth rate is, can be globally stabilized by the nonlinear damping or back-stepping approach in adaptive control. However, fundamental dif?culties arise for the discrete-time case. These dif?culties are caused by the inherent limitations of the feedback principle in dealing with uncertainties, which means that discrete-time systems with uncertainties beyond the feedback capability cannot be stabilized by any feedback control law. Today, our talk is aimed to control discrete-time nonlinear uncertain systems, in both stochastic framework and deterministic framework.