Abstract: I will discuss some recent results on the growth and decay properties of massive and massless linear scalar fields on sub-extremal Kerr backgrounds. In the massless case, in joint work with Mihalis Dafermos and Igor Rodnianski, we have established pointwise polynomial decay rates. In the massive case, we have rigorously constructed exponentially growing solutions. I will make an attempt to compare and contrast these new results with older works from the physics literature.