Since the seminal paper by Perona and Malik nonlinear diffusions have successfully been used for various image processing tasks. They also have attracted steadfast interest in the mathematical community. In this talk we will give an historical overview of the developments on the Perona-Malik equation and describe two new nonlinear diffusions which resolve the main mathematical shortcomings of Perona-Malik without sacrificing but rather enhancing the cherished practical qualities of the Perona-Malik model. The new equations, while
well-posed and purely diffusive, exhibit a non trivial dynamical behavior, which makes them mathematically interesting and practically
effective.