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In 1969, Ornstein showed that two independent, identically distributed (i.i.d.) processes with the same entropy are isomorphic, that is, there is a stationary, invertible code from one onto the other. These results have led to a number of characterizations of the class of processes which are stationary codings of i.i.d, processes. Many of these ideas are now finding a use in information theory. Some of these results and ideas are discussed, using the process language familiar to information theorists.