The amenable factors have been classified: there is a unique one of each of the types I"n", I∞, II1, II∞, IIIλ, for 0 < λ ≤ 1, and the ones of type III0 correspond to certain ergodic flows. (For type III0 calling this a classification is a little misleading, as it is known that there is no easy way to classify the corresponding ergodic flows.) The ones of type I and II1 were classified by , and the remaining ones were classified by , except for the type III1 case which was completed by Haagerup.