Mechanism Design without Money Sylvia Boicheva Abstract: Mechanism design is a field that deals with designing algorithms for making decisions based on the preferences of the agents in such a way that the outcome is guaranteed to be good for society and the agents are not incentivised to misreport their preferences. An appropriate mechanism manages to turn a group of self-interested agents into a group collectively satisfied with the decision. Most of the research on the subject is based on enforcing taxes and subsidies to compensate agents, but monetary transactions are not always applicable - for instance, buying and selling organs for transplantation is illegal. Therefore, it is important to know what can be achieved without utilizing payments. This thesis provides a broad survey of both classic and recent results in the field and points out the most important challenges and achievements.