  The task of manipulating correlated random variables in a distributed setting
has received attention in the fields of both Information Theory and Computer
Science. Often shared correlations can be converted, using a little amount of
communication, into perfectly shared uniform random variables. Such perfect
shared randomness, in turn, enables the solutions of many tasks. Even the
reverse conversion of perfectly shared uniform randomness into variables with a
desired form of correlation turns out to be insightful and technically useful.
In this survey article, we describe progress-to-date on such problems and lay
out pertinent measures, achievability results, limits of performance, and point
to new directions.
