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This article discusses some things we have learned about markets, in the process of designing marketplaces to fix market failures. To work well, marketplaces have to provide thickness, i.e. they need to attract a large enough proportion of the potential participants in the market; they have to overcome the congestion that thickness can bring, by making it possible to consider enough alternative transactions to arrive at good ones; and they need to make it safe and sufficiently simple to participate in the market, as opposed to transacting outside of the market, or having to engage in costly and risky strategic behaviour. I will draw on recent examples of market design ranging from labour markets for doctors and new economists, to kidney exchange, and school choice in New York City and Boston.