Online marketplaces have permeated many aspects of our lives, as we use them to procure goods and services of all sorts, and many have relied on them during the COVID-19 lockdowns. Both sides of the market must feel comfortable trusting each other for online marketplaces to thrive, and for that, they need to have safeguards that alleviate the problems caused by asymmetric information. In this chapter I explain how feedback and reputation systems work in practice, and how they support ecommerce in online marketplaces. It starts by covering the theory behind reputation mechanisms and how they support more efficient trade, followed by descriptions of the actual working of typical online feedback and reputation systems. A survey of empirical findings from a host of papers is presented that explore how reputation works in actual online marketplaces, and how these relate to the theory. I then highlight some of the shortcomings of feedback systems and offer some suggestions and considerations for the future design of feedback and reputation systems that can augment their effectiveness.