This paper surveys some well-known facts as well as some recent developments on the topic of stabilization of nonlinear systems. • The assumption that k(0) = 0 is quite natural; it says that no energy should need to be pumped into the system when it is at rest. The theory that results when this requirement is not imposed is also of great interest, however. • Another related interesting set of problems ("practical" stabilization) deals with bringing states close to certain sets rather than to

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... particular state x = 0. Space constraints force us to be selective in our coverage. Such selectivity will imply, as is often the case with surveys, some emphasis towards the speaker's favorite topics. Hopefully the inclusion of an additional bibliography -see the end of the paper-makes up for some of the omitted material.