What is the relationship between the conversion (1) of the elements into the (real) Body of Christ and (2) of the participants into the (mystical) Body of Christ? When we bring this and related questions to the early church, the Middle Ages, and the Reformation, we find that the conversion of the eucharistic elements has indeed been understood by unimpeachably sincere Christians in a broad variety of ways. In contrast, there has been a remarkably constant convergence regarding the all-importance of the conversion of the participants. Were this taken as the starting point, we might discover that we have much more ecumenical unity regarding the Eucharist than is usually thought to be the case.