  Within the framework of the "complexity equals action" and "complexity equals
volume" conjectures, we study the properties of holographic complexity for
rotating black holes. We focus on a class of odd-dimensional equal-spinning
black holes for which considerable simplification occurs. We study the
complexity of formation, uncovering a direct connection between complexity of
formation and thermodynamic volume for large black holes. We consider also the
growth-rate of complexity, finding that at late-times the rate of growth
approaches a constant, but that Lloyd's bound is generically violated.
