Abstract: The shortage of organs for transplants and the associated suffering has led some to suggest, that the current ban on organ sales is lifted. The thought is that we can increase the supply of organs by providing people with an economic incentive to sign up as donors (or part with a non-vital organ). While often framed as a debate for and against a market in organ this distracts from the fact that there is a great heterogeneity in the proposals put forward in this regard. The models differ, among other things, on issues such as whether there is also a market in the distribution of organs, whether there is competition among buyers and at what point the payment is made. The paper explores how the proposed models for a market procurement of organs differ. Furthermore, it presents critiques often raised against organ markets and reflects over the extent to which these critiques are relevant for the different models. '