The concept of a reconciled tree arose independently in molecular systematics, parasitology, and biogeography as a means of describing historical associations. Examples of historical associations include genes and organisms, host and parasitic organisms, and organisms and areas. A reconciled tree combines the tree for a host and its associate into a single summary of the historical association between the two entities under the assumption that no horizontal transmission of associates has occurred. In this paper, I define reconciled trees, describe an algorithm for their computation, and develop measures to quantify the degree of fit between host and associate trees. Examples are given of applying the method to gene trees and species trees, host-parasite cospeciation, and biogeography. The problem of incorporating horizontal transmission of associates (e.g., dispersal or host switching) is also addressed by introducing the concept of maximizing the amount of codivergence (shared history) between the associates.