This tutorial lecture gives a summary on the current state of the art  in the field of control of a family of inherently nonlinear systems with uncertainty, which cannot be controlled by any linear or smooth feedback, even locally.

The first part of this lecture focuses on the state feedback case.  It illustrates, via examples, when non-smooth state feedback control problems arise naturally, why non-smooth rather than smooth feedback must be employed and how to design non-smooth state feedback controllers systematically.

Output tracking and adaptive regulation will be also be discussed briefly, as a byproduct of the global stabilization results.

The second part of the talk concentrates on the more challenging situation where only the system output signal is available for feedback design. It summarizes the recent advances  in the difficult problems such as design of nonlinear higher-order observers and global output feedback controllers for a significant class of non-uniformly observable and non-smoothly stabilizable systems.