The Schwarzian derivative is one of the stranger tools in dynamics. Although this derivative has a venerable history in the field of complex analysis, it was only introduced into the study of dynamical systems in 1978. Functions with negative Schwarzian derivatives have very interesting dynamical properties that simplify their analysis. Many polynomials have negative Schwarzian derivatives. It is difficult to see geometrically what the property of negative Schwarzian derivative means. This chapter investigates how the assumption of negative Schwarzian derivative severely limits the kinds of dynamical behavior that may occur.