The Mechanism Design research group was founded in 2016 with the support of the Hungarian Academy of Sciences through its Momentum grant. Our research focus is on the algorithmic and game theoretical aspects of matching problems under preferences. This topic belongs to the interdisciplinary areas of Algorithmic Game Theory and Computational Social Choice. We have been involved in the design of real applications, including kindergarten allocations, college admissions, internship allocation and kidney exchange programmes. Currently we are participating in the design of the Hungarian kidney exchange programme, CEMS business project allocation, and we are analysing the data of the Hungarian college admissions, partly sponsored by the Cooperation of Excellences Programme of the Academy. We have been involved in international projects, such as the Matching in Practice Network (2010-), the COST Actions on Computational Social Choice (2012-2016) and on European Network for Collaboration on Kidney Exchange Programmes (2016-2020).