When Kerr black holes rotate at their maximally allowed angular velocity, they are said to be extremal. Extremal black holes display a variety of interesting phenomena that are not present in more slowly rotating black holes. I will introduce upcoming work on the existence of strong asymptotic instabilities of a non-axisymmetric nature for scalar waves propagating on extremal Kerr black hole backgrounds and I will discuss their connection with axisymmetric instabilities and late-time power law tails in gravitational radiation. If time permits, I will discuss the mechanism for deriving late-time tails and compare it with previous work on subextremal black holes.