General relativists have long made their peace with “normal” black holes, even highly spinning ones. Extremal black holes, on the other hand, namely those having the maximum spin or charge consistent with being a black hole, remain a source of extreme uneasyness. I present a series of conjectures aiming to describe the general dynamics of the Einstein equations of classical general relativity in the vicinity of extremal black holes. I will discuss how these conjectures transcend older paradigms concerning extremality and near-extremality, in particular, the so-called “third law of black hole thermodynamics”, which viewed extremality as an unattainable limit, and the “overspinning/overcharging” scenarios, which viewed extremality as a harbinger of naked singularities. Finally, I will outline some of the difficulties in proving these conjectures, discuss some work which has been done in this direction, and speculate on what it could mean if the conjectures turn out not to be true.