This book addresses the debate usually tagged as being about 'markets in human body parts' which is antagonistically divided into pro-market and anti-market positions. The author provides a set of propositions about how to approach this and shows a way out of the concrete impasse of it. Assumptions about markets and bodies that characterize this debate are analyzed and described while the author argues that these assumptions are in fact constitutive for exchanges of human bodily material - but in unacknowledged ways. It is concluded that what we need is a different analytical approach to better understand the mechanisms at play when organizations exchange organs, tissues and cells for use in transplantation and fertility medicine. Assumptions about markets and bodies that characterize this debate are analyzed and described while the author argues that these assumptions are in fact constitutive for exchanges of human bodily material - but in unacknowledged ways. It is concluded that what we need is a different analytical approach to better understand the mechanisms at play when organizations exchange organs, tissues and cells for use in transplantation and fertility medicine.