Readers familiar with Marilyn Adams's work know to expect top quality analytical philosophical rigour combined with a respectful historical approach to medieval thought. This survey of eucharistic theology, with special attention to the mechanics of the real presence of Christ in the consecrated bread and wine, provides an overview of the most influential theologians of the late thirteenth and early fourteenth centuries. Ordinarily, this topic's complexity discourages many readers; Adams's aim is to provide a concise, accurate introduction, which she accomplishes effectively. She provides an introduction to the basic elements of Aristotelian theories of body and place, followed by a neat summary of the medieval conception of a sacrament, and a survey of the theologians’ accounts of how sacraments have causal efficacy in changing material objects (both sacramental elements, like the baptismal water, chrismatic oil, and the consecrated bread and wine, and the Christians who receive them). The reader is now ready to explore how these thinkers handled the challenge of explaining transubstantiation, the doctrine according to which the consecrated bread and wine become the real body and blood of the ascended, living Christ, while apparently remaining what they were beforehand. The key is to explain the ‘real presence’ of the incarnate God in the creatures of bread and wine sufficiently to take into account thorny philosophical problems. These include explaining how one being can be in several places at once, describing creation and annihilation using a physics to which both concepts are foreign, as well as the referent of ‘hoc’ in ‘hoc est corpus meum’. Adams provides an effective introduction to Thomas's explanation of how one thing is converted into something else in transubstantiation, ‘absolute whole being conversion’, as she describes it. Next she describes Giles's shift in approach, in which a Thomistic account of conversion is generally accepted, and theology is employed to account for possible impossibilities that lurk in the shadows. This section is particularly useful, because secondary work on Giles's eucharistic theory is scant. Scotus rejects Thomas's description, and employs a distinction between kinds of position and real presence in terms of external relation. Further, he distinguishes between two kinds of transubstantion: productive and translative, the former describing the new existence of a thing, and the latter the translation of an extant thing to a new substantial location. Finally, Adams describes Ockham's shift of the discussion from substance to quantity. The next section of the book addresses problems associated with the relation of accident to substance that arise from these theories, and the final section analyses the application of this complex metaphysics to the function of a sacramental meal. In sum, Adams has written a concise, analytically clear survey of some of the most important eucharistic theologies of the medieval period. My only concern is that the bibliography is limited regarding more philosophically developed studies of individual thinkers; for example, she does not mention that J. J. M. Bakker's two-volume La Raison et le miracle (1999), remains the definitive study of the development of eucharistic theology in the thirteenth and fourteenth centuries. Adams's introduction provides the wherewithal for philosophers in particular to approach that work, but does not take its place.