  In this paper we review the predictions of the replica approach on the
probability distribution of the overlaps among replicas and on the sample to
sample fluctuations of this probability. We stress the role of replica
equivalence in obtaining relations which do not depend on the form of replica
symmetry breaking. A comparison is done with the results obtained with a
different rigorous approach. The role of the ultrametricity and of other
algebraic properties in discussed. It is shown that the ultrametric solution
can be obtained from a variational principle.
