The distance between operator algebras on the same Hilbert space is the Hausdorff distance between their unit balls, and we say that two algebras are close if this distance is small. Kadison and Kastler studied this distance and raised the question of whether sufficiently close algebras had to be isomorphic, or even unitarily equivalent (perhaps with a unitary close to the identity). Early examples showed that isomorphism could fail for close nonseparable nuclear algebras, while even if a unitary equivalence were possible, no choice of unitary close to the identity could work. Thus, in the nuclear realm, the strongest form of the question is whether close separable nuclear algebras are unitarily equivalent. I will present a positive solution to this. This is joint work with Erik Christensen, Allan Sinclair, Stuart White and Wilhelm Winter.