A dynamical system $(X,T)$ is completely scrambled if all non-diagonal
pairs $(x,y)\in X\times X$
are proximal (i.e. $\liminf_{n\to \infty} d(T^n(x),T^n(y))=0$) but not
asymptotic (i.e. $\limsup_{n\to \infty} d(T^n(x),T^n(y))>0$).
In this talk we will survey recent progress on characterization of
such systems and their additional dynamical properties.