In this talk we survey our recent results concerning transformations of different kinds of structures on the positive definite cones of $C^*$-algebras. We will present precise descriptions of various algebraic isomorphisms, mean preservers, surjective isometries, etc. It will turn out that all those transformations of the positive definite cones are closely connected to the $C^*$-isomorphisms (or Jordan *-isomorphisms) of the underlying algebras.